Reconstruction Quality

Cranial implant generation is an important task in medical imaging. Recent point cloud based generative methods, particularly flow matching, offer strong reconstruction quality and efficient sampling, but still require multiple neural function evaluations during inference. This limits rapid generation of multiple plausible implant candidates. We propose Teacher-guided Endpoint Distillation (TED), a simple one-step distillation framework for conditional cranial implant generation on point clouds. TED trains a one-step student using teacher-guided endpoint supervision and geometric matching losses, while avoiding explicit path straightening. We evaluate TED on the SkullFix and SkullBreak benchmarks. TED achieves the best overall performance on the SkullBreak dataset, remains competitive on SkullFix, and provides the strongest Chamfer distance performance among the compared one-step methods. In addition, TED generates implants in approximately 0.04s per sample. These results show that one-step distillation can substantially accelerate conditional point cloud implant generation without sacrificing reconstruction quality.

We introduce Complex-Valued Quadratic Phase Gaussian (CVQPG), a novel hologram representation method that replaces standard 2D Gaussian representations used in 2D Gaussian Splatting with 2D quadratic phase functions. CVQPG incorporates additional learnable parameters to control the curvature of these bases. We evaluate our approach against state-of-the-art methods, exceeding the visual quality by +0.19 dB (RGB) and +0.33 dB (grayscale) on average in holographic reconstructions. Specifically, our equal parameter count evaluations show that modulating the primitive's wavefront is an effective and lightweight enhancement for hologram representations. In addition, our frequency domain analysis illustrates that CVQPG has successfully preserved the mid-to-high frequency band of natural images.

Multi-contrast MR scans contain redundant structural information that can be leveraged during reconstruction and potentially accelerate acquisition times. This idea has inspired end-to-end guided reconstruction models, leveraging one or more contrasts to guide the reconstruction of a different contrast. However, these models require large paired multi-contrast raw datasets for training, limiting their application in low-data regimes. In this work, we propose a modular framework, namely CoSMo-RecNet, for learning guided reconstruction models in the low-data regime. At its core is a reusable multi-contrast representation based on a content/style model, which can be learned from large-scale, publicly accessible, unpaired multi-contrast image datasets, without available k-space data. Using this frozen model as a multi-contrast prior and using a set of reference contrasts, the reconstruction problem reduces to a much simpler refinement problem that can be solved by a lightweight unrolled network and thus learned from small, task-specific reconstruction datasets. We demonstrate the efficacy of CoSMo-RecNet by evaluating it on the low-field 0.3 T M4Raw dataset, showing stable reconstruction quality on decreasing the raw training data budget. CoSMo-RecNet achieved higher reconstruction quality with 5 training subjects or lower compared to a parameter-count-matched MoDL trained on 100 subjects. On a data-limited and severely out-of-distribution ultra-low-field 47 mT Halbach scanner dataset, CoSMo-RecNet was superior to other viable strategies, including classical reconstruction, transfer learning, and zero-shot reconstruction.

Digital restoration of historical manuscript images aims to improve readability while preserving the authenticity of cultural heritage documents. However, evaluating quality of restored manuscripts remains challenging, where readability is often subjective and expert annotations are scarce. This study investigates the suitability of contrast-based image quality measures to assess quality and legibility of reconstructed manuscript images from multi-spectral imaging. Two experiments were conducted with publicly-available data sets, facilitating manual quality scores by experts and full-reference image quality measures as reference evaluations. The results show that potential contrast achieves the highest correlation with expert ratings, while contrast-to-noise ratio demonstrates the strongest agreement with full-reference quality measures. Overall, contrast-based measures consistently outperform general image quality measures, demonstrating their potential as objective indicators of manuscript legibility and reconstruction quality.

Cone-beam computed tomography (CBCT) enables volumetric reconstruction from X-ray projections, but suffers from severe artifacts--especially beam hardening--when imaging materials with high attenuation such as metals. These artifacts arise from the polychromatic nature of X-rays and are not properly addressed by conventional monochromatic reconstruction algorithms. While recent neural representation-based methods offer improved reconstruction quality, they are computationally expensive and often impractical for deployment. We propose a novel physics-inspired, self-calibrating metal artifact reduction method that efficiently reconstructs 3D CBCT volumes while correcting beam hardening artifacts. Our method integrates a polychromatic X-ray projection model, material-dependent attenuation profiles, and system response modeling into a Gaussian Splatting framework. Unlike prior work, we eliminate the need for manual metal masks or strong prior assumptions, and we optimize both reconstruction parameters and X-ray spectral characteristics jointly during training. We further introduce a high-fidelity synthetic CBCT dataset generation pipeline validated on Monte-Carlo x-ray simulation toolbox and release new datasets with severe metal-induced artifacts to support the community. This is the first splat-based method for reducing beam hardening in CBCT. Extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art approaches in artifact suppression and reconstruction accuracy.

Sparse voxel reconstruction offers an efficient representation for high-fidelity 3D modeling, yet its geometry is commonly optimized from local photometric evidence and discrete visibility statistics. This often leads to fragmented surfaces, excessive subdivision, and floating artifacts, particularly in weakly textured or sparsely observed regions. We introduce SurfSVR, a novel sparse voxel reconstruction paradigm that treats 2D surface priors as explicit 3D geometric regularizers. Instead of directly lifting noisy pixel-wise depth predictions, SurfSVR first organizes each image into coherent surface regions by jointly reasoning over appearance, monocular depth, normals and cross-view geometry. Each region is then represented by an adaptively selected planar or quadratic surface model based on fitting reliability and geometric complexity, while cross-model agreement distinguishes reliable geometry from ambiguous predictions. These structured 2D priors are lifted into 3D and integrated throughout the reconstruction pipeline. They guide surface-adaptive voxel subdivision, provide region-level depth and normal supervision during optimization, enhance geometrically reliable sparse-observed surfaces in voxel pruning, and suppress off-surface floaters during post-refinement training. This unified design converts semantic and geometric coherence in image space into persistent structural constraints in 3D. Extensive experiments on 3 public benchmarks demonstrate that SurfSVR consistently improves sparse voxel reconstruction across scenes with substantially different visibility and geometry characteristics, achieving state-of-the-art reconstruction quality. Codes and models will be released soon.

The acquisition of multispectral imagery via small satellites (e.g., CubeSats) presents significant data downlink challenges due to high data volumes and restricted communication windows. While onboard image compression is critical to address this bottleneck, traditional methods often struggle to adapt to the nonlinear statistics of multi-band, multi-resolution data. To overcome these limitations, we propose ELMZip, a novel framework based on Extreme Learning Machines (ELM) and domain decomposition strategies for efficient, resolution-free onboard neural representation. ELMZip formulates the fitting process as a convex least-squares problem using random-feature single-layer networks, thereby eliminating the need for computationally expensive backpropagation. By adopting an asymmetric transmission protocol that sends only the compact output weights, the proposed method significantly reduces the downlink payload. Unlike previous neural representation approaches that rely on iterative optimization and require transmitting full network parameters, ELMZip achieves significant compression efficiency while maintaining high reconstruction fidelity. This capability enables immediate image reconstruction for analysis, allowing resource-constrained platforms to maximize data return and advancing real-time AI-powered Earth observation.

3D Gaussian splatting (3DGS) has emerged as a widely-used tool for novel view synthesis, offering real-time rendering in a sparse representation. However, the method's reliance on structure-from-motion initialization and photometric optimization can lead to suboptimal geometric reconstruction, particularly for objects with high specularity. In this work, we investigate the integration of geometric priors, in the form of predicted normal and depth maps, into the 3DGS framework to improve the reconstruction quality. We analyze the effect of incorporating these priors into GS-based methods and our evaluation reveals that multi-view predictions, as they are done by the recent visual geometry grounded transformer (VGGT), outperform single-view alternatives. A major factor is the existence of a confidence map for the estimations, which comes as a by-product of multi-view models and which can significantly improve the effectiveness of priors by weighting each prediction appropriately. Extensive experiments on standard benchmarks show consistent improvement in reconstruction quality and significant gains in complex scenes including specular objects.

Unmanned aerial vehicle (UAV) photogrammetry requires camera networks that provide sufficient surface coverage, image overlap, parallax, and resolution, yet conventional flight patterns are often poorly adapted to scene geometry resulting in local reconstruction errors. This paper proposes an iterative hybrid discrete-continuous viewpoint planning method for targeted UAV photogrammetry from a proxy reconstruction. The method scores sampled surface points using photogrammetric heuristics based on frontality, imaging distance, parallax, and multi-view observation count, while also evaluating the full viewpoint set in terms of visibility, pairwise overlap, and graph connectivity. Candidate viewpoints are generated around weakly observed regions, refined using clustered Covariance matrix adaptation evolution strategy (CMA-ES) optimisation, and removed when redundant. The final flight path combines close-range detail viewpoints with wider model-coverage viewpoints, balancing local reconstruction quality with global image-network robustness. Evaluation on three synthetic scenes shows that the proposed method improves both reconstruction accuracy and completeness compared with prior UAV path-planning methods.

Old photographs often suffer from multiple coupled degradations, including scratches, cracks, fading, blur, noise, and missing regions, severely degrading both visual quality and semantic content. We propose Loop-Mamba, a lightweight loop-based state-space framework that formulates old photo restoration as progressive state evolution, where a persis- tent restoration state is continuously propagated and refined through iterative computation. Specifically, we introduce a Semantic-Guided Degradation Estimator (SGDE) to explicitly model heterogeneous degradations by jointly predicting local degradation maps and global degradation scores, providing degradation-aware guidance for state evolution. We further develop a Shared Structural Memory Mamba (S$^2$M- Mamba), which maintains a persistent restoration state across iterations, enabling persistent state evolution through shared structural memory for robust long-range structural reconstruction. Benefiting from first-order state recursion, Loop-Mamba propagates latent restoration states through recurrent tran- sitions instead of repeatedly stacking deep feature transformations, thereby alleviating gradient dilution while avoiding the computational overhead inherent in iterative CNN- and Transformer-based restoration frameworks. A lightweight multi-directional scanning strategy further enhances direc- tional information aggregation and preserves structural continuity. To better evaluate restoration quality, we introduce the task-oriented Old Photo Damage Recovery Score (ODRS), which jointly measures degradation recovery and structural reconstruction fidelity. Experimental results on the public SynOld benchmark demonstrate that Loop-Mamba consistently outperforms previous state-of-the-art methods across both conventional restoration metrics and the proposed ODRS.

3D reconstruction of unknown environments is a key application in robotics but is severely limited by the computational and energy capabilities of current aerial platforms. Deploying multiple UAVs and providing efficient and scalable path planning strategies are common approaches, but effective online coordination among UAVs remains a significant challenge. To address this problem, we propose a quality-adaptive decentralized decision-making strategy to build a 3D map with user-defined degrees of fidelity. The approach integrates a quality-oriented criterion based on TSDF confidence into view generation and information gain estimation to produce viewpoints consistent with the desired fidelity target. Additionally, we employ two levels of coordination: a penalty factor in the viewpoint evaluation to encourage local dispersion among the UAVs and a global imbalance correction mechanism. The latter, based on regularized clustering and optimal task assignment, is only triggered when an unbalanced configuration relative to high-information regions is detected. Simulation results demonstrate that the proposed method improves path efficiency compared to state-of-the-art multi-UAV exploration approaches, while also achieving higher-fidelity reconstructions in terms of coverage and accuracy. We make our code publicly available to the community.

The Discrete Fourier Transform, the Discrete Cosine Transform, and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: they run in near-linear time (linear up to a polylogarithmic factor), they are exactly invertible, and they carry few to no parameters. In this work, we generalize these bases to isometric multilinear bases, allowing a small number of extra parameters, polylogarithmic in the image size, while preserving all three properties. Given an image dataset, we develop a systematic framework that searches this family for the basis compressing the dataset most effectively: the basis is parameterized as an isometric tensor network, inspired by quantum many-body theory, and trained with Riemannian optimization on the manifold of unitary matrices. Across natural photographs and line drawings, the trained bases consistently improve on their fixed, non-parametric counterparts. On Quick Draw line-drawing compression, they store images in roughly $20\%$ fewer bytes than JPEG's $8 \times 8$ block cosine transform at the same reconstruction quality.

Dynamic scene reconstruction with 3D Gaussian Splatting requires a balance between fine-grained motion modeling, structural stability, and compact representation. Existing per-primitive methods provide flexible local deformation but often suffer from redundant primitive growth, while anchor-based methods improve spatial regularity at the cost of suppressing locally varying motion. To address these issues, we present GrainGS, a dynamic Gaussian framework that combines a hierarchical anchor scaffold with per-Gaussian deformation. A static warm-up stage first establishes a time-invariant canonical representation from observations across all timestamps. During joint training, a stop-gradient operation blocks the deformation-mediated gradient pathway to the canonical positions while preserving their direct refinement through the reconstruction objective. Each Gaussian then predicts independent temporal offsets for position, rotation, and scale, enabling detailed local motion within a structurally constrained scaffold. A canonical-residual appearance decomposition further models frame-dependent photometric changes without forcing them into geometric deformation. Experiments on synthetic monocular and real-world multiview benchmarks show that GrainGS achieves high reconstruction quality, real-time novel view synthesis, and compact storage. Under the synthetic benchmark setting, it reaches an average peak signal-to-noise ratio of 36.98 decibels, renders at 435.6 frames per second, and requires 4.67 megabytes of storage.

Weakly supervised pipelines for medical imaging have become increasingly popular over the years. These systems often include multiple stages and components, such as reconstruction, generation, and localization, yet standard evaluation metrics provide limited insight into whether clinically relevant information is preserved across each stage. We present the diagnostic gap framework, a practical evaluation tool that measures decision preservation and explanation preservation as a function of measured reconstruction fidelity. To isolate the effect of reconstruction from localization, we evaluate on curated lesion ROI crops using a fidelity ladder of three class-conditional reconstructors---VQ-VAE-GAN, VAE-GAN, and diffusion (SDEdit)---spanning a twenty-fold range in perceptual distance (LPIPS 0.029--0.584). At autoencoder fidelity, both decision and explanation are preserved: AUC changes remain within $\pm$0.005 and attribution similarity (HiResCAM, Grad-CAM++) stays high. At diffusion fidelity, both collapse: pooled AUC drops by 0.253 and mass-pathology AUC falls below chance. The diagnostic gap is thus a measurable function of reconstruction fidelity rather than an intrinsic cost of reconstruction, and the framework provides an architecture-agnostic instrument for identifying when and where multi-stage pipelines lose diagnostic signal.

Reconstructing animatable 3D human avatars from monocular video is a fundamental problem in computer vision with broad applications in AR/VR and digital content creation. Existing approaches typically couple parametric body models with neural rendering or 3D Gaussian splatting and optimize all body regions jointly from short videos, which often degrades fidelity in the visible areas. To overcome this limitation, we introduce FlexiAvatar, a unified framework that explicitly optimizes only the visible body regions, effectively eliminating artifacts arising from unobserved limbs. Our method integrates occlusion-robust SMPL-X tracking with part-specific residual refinement to capture high-frequency geometric and appearance details. To complete entirely unseen regions (e.g., back views), we leverage a diffusion-based approach to generate texture consistent with the observed appearance. Experiments on full-body (NeuMan, ZJU-MoCap, WildAvatar), upper/half-body (talk-show clips), and head-only (INSTA) inputs show that FlexiAvatar delivers consistently higher reconstruction quality, outperforming state-of-the-art methods by an average PSNR improvement of approximately 3% across datasets. Finally, by restricting optimization to observed regions, our method reduces the effective number of Gaussians that must be optimized and rendered, leading to reduced runtime and memory overhead in partial-visibility scenarios.

Super-resolution can make inspection images appear sharper without preserving the evidence needed to detect a defect. We study this failure mode with a benchmark that separates reconstruction from detection and evaluates both at a predeclared low false-positive rate. Ten end-to-end repetitions combine independently generated line/space and contact-hole images with model training, calibration, clean controls, weak defects, and a held-out defect morphology. Every reconstruction is scored by the same local residual detector, while direct and jointly trained detectors form a separate comparison track. Reconstruction fidelity and inspection utility diverge: the two learned reconstruction models attain the highest structural similarity yet detect fewer defect pixels than bicubic interpolation in every paired repetition. A direct DeepLabV3 detector reaches $0.1984\pm0.0385$ recall at $0.000174\pm0.000084$ false-positive rate and satisfies the held-out feasibility criterion in all ten repetitions. An illustrative joint model, DPU-WaferSR, passes independent clean calibration but exceeds the held-out limit in all ten repetitions, demonstrating that calibration success does not guarantee transfer. Weak-defect recall remains near zero for every feasible method. Applying the unchanged policies to 4,591 public Carinthia-S masks further reveals large method-dependent shifts on real SEM texture. These results support a simple conclusion: super-resolution for inspection should be judged by preserved task evidence and operating-point transfer, not reconstruction quality alone.

Whole-slide images (WSIs) provide rich tissue-level and cellular-level information, but storing and transmitting high-magnification pathology data is resource-intensive. Moreover, annotating WSIs at the pixel level is labor-intensive and time-consuming. Therefore, it is important to investigate whether low-magnification pathology images with limited annotations (i.e., image-level instead of pixel-level labels) can achieve performance comparable to high-magnification images. This paper presents a systematic benchmark study on weakly supervised histopathological image segmentation under different low-resolution storage settings. Starting from high-resolution image patches, we simulate lower-magnification inputs and reconstruct them to the original size using interpolation and deep learning-based reconstruction methods before applying the weakly-supervised segmentation pipeline. This framework enables a quantitative evaluation of how weakly supervised methods respond to different levels of resolution degradation. Experimental results show that reconstruction quality metrics alone are insufficient to predict downstream segmentation performance. In particular, the study identifies a critical degradation point where the localization of small-scale structures declines significantly. These findings provide practical guidance for designing efficient digital pathology storage systems while maintaining reliable automated analysis. Code is available at https://github.com/Dung-Dx/LowMagWSS

Implicit neural representations (INRs) offer compact encoding of volumes, but as lossy approximators, inevitably have prediction errors. We consider INRs that can simultaneously encode relative error scales by predicting distributions using tools from uncertainty estimation. Typically, uncertainty estimation relies on computationally expensive approaches or on predefined parametric assumptions about the predictive distribution (e.g., Gaussian). In this study, we propose a lightweight method that reformulates regression-based INR training as a classification task by discretizing continuous targets into bins, enabling flexible distribution modeling to capture complex multimodal behaviors. We analyze the trade-off between regression and classification for INR training and demonstrate that the classification setting tends to achieve high reconstruction quality and competitive error awareness through uncertainty estimation, compared to regression-based approaches.

We study why diffusion autoencoders can achieve similar image quality while learning substantially different latent structures. We trace this behaviour to optimisation dynamics; we analyse curves of image reconstruction against latent representation quality, revealing trajectories that organise around two distinct regimes early in training. Models in the reconstruction regime prioritise image fidelity early, whereas those in the disentanglement regime improve reconstruction and disentanglement more gradually. We hypothesise that this behaviour can be influenced by targeting shortcut pathways in the diffusion U-Net and controlling early noise-level exposure, thereby shaping the reconstruction-disentanglement trade-off during training. To steer optimisation toward stronger representations, we introduce SteeringDRL, combining gated residual U-Nets with a simple noise-level exposure curriculum for training. Across disentanglement benchmarks, SteeringDRL improves representation quality and reduces seed sensitivity. Our method further extends to spatial disentanglement in object-centric learning, improving segmentation quality on synthetic and real-world datasets.

Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets. This mismatch can limit reconstruction accuracy, reduce sample quality, and constrain the expressive power of the learned latent space. We propose the eXact-Prior Variational Autoencoder (X-VAE), a framework that replaces the conventional standard normal prior with a Gaussian prior derived from the latent representations of a pretrained autoencoder (AE). Specifically, the empirical mean and standard deviation of the AE latent codes are used to parameterize a data-adaptive prior that more closely reflects the underlying structure of the training data. During generation, X-VAE introduces a latent scaling factor that enables explicit control over the variance of the sampled latent vectors, providing a simple mechanism for balancing sample diversity and fidelity. This flexibility makes the proposed approach particularly well suited for applications such as industrial and engineering design, where generated solutions must satisfy strict structural or functional constraints while still permitting meaningful design exploration. We present the mathematical formulation of well-suited X-VAE, derive the corresponding KL divergence objective for the proposed prior, and evaluate the method on standard benchmark datasets. Experimental results demonstrate that X-VAE preserves reconstruction quality while producing latent representations that better align with the empirical data distribution, leading to improved controllability and more realistic generated samples.

Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data. Existing algorithms for computing TT decompositions can be categorized into two main types: conventional batch-based approaches and recursive online methods. In the context of streaming data, batch methods typically achieve higher reconstruction accuracy but often suffer from memory exhaustion, while online methods provide greater computational efficiency. In this work, we introduce Online TT-ALS (Alternating Least Squares), an algorithm that sequentially enforces orthogonality constraints. This approach allows for efficient and exact updates of the core tensor while maintaining high reconstruction accuracy. Theoretically, we prove that enforcing these orthogonal gauge constraints guarantees monotonic decrease of the local objective function and temporal smoothness. Computationally, our deterministic single-sweep update reduces the rank dependence from quadratic to linear, achieving an overall complexity of $\mathcal{O}(I^{n-1} r)$. Experimental results demonstrate that the proposed method outperforms existing online techniques not only in terms of mathematical approximation accuracy but also in human perception-based video quality metrics. Furthermore, compared to recent deep learning-based paradigms, our algebraic approach achieves speedups of several orders of magnitude. Consequently, our method exhibits high computational efficiency and is suitable for low-latency real-time processing applications.

3D anomaly detection in point clouds is critical for high-precision industrial manufacturing. Reconstruction-based methods have laid a strong foundation by detecting 3D anomalies through comparisons between defective inputs and their reconstructed normal counterparts. However, existing methods still suffer from two challenges: 1) the foreground weak defective regions such as scratches are hard to reconstruct and detect, where the anomaly deviations in normalized point clouds can be as small as $10^{-3}$; 2) the background non-defective regions are prone to get positional bias in reconstruction, which leads to false positives. To address these challenges, we propose \textbf{PCDiff}, a point cloud diffusion framework for instance-level 3D anomaly generation and detection. In the generation phase, an instance-level multi-modal attention is embedded into the generation framework, where anomalies are conditioned with texture gradient, image patch, text and mask. The instance-level condition enables the high-quality generation of weak-defective anomalies. In the detection phase, a joint local-global reconstruction algorithm is introduced to ensure local anomaly restoration and global geometric consistency, which preserves background normal structure while restoring the foreground defect. Extensive experiments demonstrate that the proposed PCDiff significantly outperforms state-of-the-art methods in both 3D anomaly generation fidelity and reconstruction quality, leading to substantial improvements in anomaly detection accuracy.

Visual Geometry Grounded Transformer (VGGT) has already attracted a great deal of attention in a short period of time, not least due to the Best Paper Award at CVPR-2025. Similar to DUSt3R and MASt3R, VGGT aims to bring about a paradigm shift by replacing established methods like bundle adjustment and feature matching with a simple, unified, feed-forward neural network that predicts camera poses, depth maps, and dense 3D structure directly from multiple images of a scene in a few seconds. A key aspect is its ability to process an arbitrary number of views consistently in a single forward pass without any post-processing or iterative optimization. For photogrammetry, this opens new possibilities for real-time, scalable, and accessible 3D reconstruction. In this context, not only high reconstruction accuracy but also high-quality uncertainty estimates are crucial, as they foster trust and enable robust quality assurance. This paper therefore investigates the quality of VGGT's uncertainty predictions. The analysis identifies an effective confidence threshold for filtering VGGT's raw output and demonstrates that enhancing uncertainty quality holds strong potential for improving the accuracy of its 3D reconstructions.

Accurate quantification and uptake measurement in PET are critical for assessing disease progression and supporting clinical decision-making. While high-count PET provides reliable image quality, the associated radiation dose and prolonged acquisition remain significant clinical concerns, motivating the adoption of low-count protocols. Diffusion-model-based methods have demonstrated strong potential for restoring low-count PET to near high-count quality, but their iterative sampling procedure becomes prohibitively expensive when applied to high-resolution 3D PET volumes, introducing substantial inference latency that limits practical clinical deployment. To address these challenges, we propose a training-free Global-Local Skipping Strategy that accelerates diffusion model-based 3D PET denoising while simultaneously improving reconstruction quality. The proposed method is plug-and-play and directly applicable to pre-trained diffusion models without retraining or architectural modification. Specifically, we introduce: (i) a global denoising step skipping strategy that initializes the reverse diffusion process from an intermediate denoising step using a noise-consistent transformation of the low-count input, substantially reducing the number of required denoising steps; and (ii) a local feature reuse shortcut that reuses slowly-varying high-level U-Net features across neighboring denoising steps, further reducing per-step computation while preserving image fidelity. We evaluate the proposed approach on multiple PET tracers from in-house and public datasets, including 18F-FDG PET, 68Ga-DOTATATE PET, and 18F-PSMA PET, demonstrating consistent acceleration of over an order of magnitude alongside improved or comparable reconstruction performance relative to the full-step baseline. Blinded reader studies further confirm enhanced clinical confidence and perceived diagnostic quality.

Point Cloud Quality Assessment (PCQA) methods typically predict scalar Mean Opinion Scores (MOS), which quantify overall perceptual degradation but do not reveal its causes. In contrast, human observers naturally reason in terms of specific distortions such as blur, color shifts, point density changes, missing regions, and geometric deformations. To close this gap, we introduce DAL-PCQA, a distortion-aware, language-annotated dataset for PCQA. DAL-PCQA augments benchmark point clouds with multi-level distortion severity labels, discrete quality categories, and structured natural language descriptions aligned with human perception. We define a point-cloud-specific distortion taxonomy that covers both photometric and geometric artifacts. Statistical analysis reveals characteristic degradation patterns across distortion types and quality levels. To assess the utility of these annotations, we compare zero-shot and fine-tuned multimodal models for generating perceptual quality descriptions. Experiments show that distortion-aware supervision substantially improves lexical and semantic alignment with ground-truth descriptions. By enabling interpretable, distortion-level reasoning, DAL-PCQA facilitates language-driven, explainable point cloud quality assessment. The dataset is publicly available at https://github.com/swarna96/DAL-PCQA.

In AI for Science, physics-informed losses are increasingly used to train learned compressors for scientific data, but their rate-distortion implications remain poorly understood. At fixed bitrate, these objectives often improve preservation of a target physical observable while degrading standard reconstruction fidelity. We develop a local geometric theory showing that this tradeoff is governed by the interaction of latent-space sensitivities induced by the entropy model, the physical observable, and the distortion metric. At each operating point, these induce preferred directions along which compression noise should be suppressed, yielding an anisotropic error-allocation mechanism. When these directions are misaligned, improving the observable at fixed rate necessarily worsens standard distortion, establishing a fundamental limit on simultaneous preservation. We formalise this through a local tangent-space rate-distortion law and introduce a practical alignment diagnostic based on dominant eigenspace overlap. Experiments across scientific domains test the theory and validate that the alignment diagnostic correlates with observed data- and physics-space trade-offs.

This paper studies the problem of inverting the DDIM image generation process to recover latent variables, particularly the initial noise map, from a generated image. Existing methods often struggle with accuracy in this task. We propose a novel hybrid approach that combines direct inversion via gradient descent for the first step, followed by a fixed-point method for subsequent steps. Empirical evaluations across three datasets demonstrate that our method significantly improves the prediction of initial latent variables while achieving superior reconstruction accuracy. Additionally, we introduce a new evaluation, called the self-interpolation test, which assesses the quality of images generated from interpolated points between the true and predicted latent maps, offering deeper insights into performance. Our results reveal that while existing methods perform reasonably well in reconstruction, they consistently fail to accurately predict the initial latent variables, resulting in poor performance on the self-interpolation test. In contrast, our method outperforms all others across all metrics, providing valuable insights into diffusion models and enhancing their applications in image generation and editing.

Dynamic scene reconstruction via 3D Gaussian Splatting (3DGS) has emerged as a compelling approach for representing evolving environments, yet understanding trade-offs between methodologies remains crucial. This paper presents a comprehensive analysis of dynamic 3DGS methods, categorizing them into two paradigms: structure-guided methods employing auxiliary representations (deformation fields, canonical spaces, grids) to model temporal changes, and gaussian-centric methods encoding dynamics directly into primitives via continuous functions or 4D representations. We evaluate representative methods from both paradigms on the D-NeRF benchmark. Our findings reveal that structure-guided methods achieve superior reconstruction fidelity and compact model sizes, while gaussian-centric approaches demonstrate significantly higher rendering speeds enabling real-time performance, though with greater quality variability and potentially substantial storage overhead. This analysis highlights a fundamental trade-off between reconstruction quality/compactness versus rendering speed, providing insights to guide future research and application development in dynamic scene reconstruction.

Compositional implicit surface representations model scenes as collections of objects, each encoded by a Signed Distance Field (SDF). A fundamental limitation of this approach is that multiple SDFs can produce geometries that interpenetrate, violating physical plausibility. Existing mitigation strategies rely on soft penalty terms that reduce but do not eliminate intersections, and require careful loss weighting. To truly prevent interpenetration, we propose a hard constraint on vector-valued SDFs and introduce S2MDF, a lightweight plug-and-play module that enforces the constraint on any object-compositional SDF representation without architectural modifications. It introduces negligible computational overhead and is compatible with linearly-interpolated standard meshing algorithms such as Marching Cubes. It can be applied during training or as a post-processing step. Experiments on multiple state-of-the-art compositional methods show that S2MDF reduces intersections to numerical precision while preserving reconstruction quality, outperforming existing mitigation strategies.

Image quality in modern imaging systems emerges from the coupled effects of the sensor, optics, and computational reconstruction. Ultra-thin metalenses offer a path toward substantial miniaturization of optical modules, but practical designs often exhibit pronounced chromatic and field-dependent aberrations that necessitate computational reconstruction. In current metalens pipelines, reconstruction models are commonly trained and selected using distortion-based fidelity objectives, such as PSNR, yet these proxies can be weakly correlated with human preference and downstream utility, reflecting the well-known perception--distortion trade-off. We introduce MetaRanker, a human-in-the-loop active ranking framework that formalizes metalens image quality in terms of semantic interpretability, defined as the degree to which humans can reliably recognize objects and structures in the presence of optical artifacts. MetaRanker combines a probabilistic preference model with uncertainty-aware query selection, and leverages vision--language models to provide lightweight semantic priors. Importantly, these priors are used only to guide the sampling of informative comparisons; human judgments remain the primary supervision signal throughout. Across real-world and synthetic metalens datasets with distinct degradation profiles, MetaRanker produces rankings that align most closely with human assessments, while reducing the number of pairwise annotations required by approximately 80% relative to exhaustive pairwise evaluation. Finally, we show that standard image quality assessment metrics exhibit limited alignment with human interpretability in the metalens domain, positioning MetaRanker as a practical step toward perceptually grounded metalens evaluation and co-design.

We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.

Image semantic communication is a critical component in next-generation wireless communication systems. However, such systems typically suffer from large memory footprints and high computational complexity, making them difficult to deploy on resource-constrained devices. To address these challenges, we propose a vision transformer (ViT)-enabled image semantic communication system. In this system, a recursive structure is introduced to iteratively refine semantic features and reduce the parameter count. In addition, three dynamic adjustment strategies are designed to adaptively reduce computational complexity: dynamic depth adjustment, dynamic width adjustment, and joint width-depth optimization. Dynamic depth adjustment adaptively determines the number of recursive modules according to image content and channel conditions, while dynamic width adjustment selectively preserves important neurons and attention heads. The joint width-depth optimization further enables flexible computation configurations. Simulation results verify that the proposed recursive ViT-based system, combined with the three dynamic adjustment strategies, reduces the parameter count by 48.7% and achieves higher reconstruction quality than existing baselines under comparable computational complexity.

State space models (SSMs) have emerged as a powerful paradigm for efficient single-image super-resolution (SR) due to their linear complexity and long-range modeling capabilities. However, existing Mamba-based methods typically rely on data-agnostic rigid scanning, which reshapes 2D images into 1D sequences over a fixed grid, inevitably disrupting spatial-semantic topology and introducing artifacts. Inspired by the \textbf{Gestalt perceptual grouping theory}, we propose \textbf{SP-MoMamba}, a superpixel-driven mixture of state space experts designed for content-aware SR. Our core idea is to transform the traditional rigid scanning into a \textbf{semantic-level interaction} by treating superpixels as fundamental units. Specifically, we introduce the \textbf{Superpixel-driven State Space Model (SP-SSM)}, which compresses semantically homogeneous regions into high-order tokens to preserve global topological consistency. To address the conflict between fixed scanning scales and diverse semantic granularities, we develop the \textbf{Multi-Scale Superpixel Mixture of State Space Experts (MSS-MoE)}. This module utilizes a dynamic routing mechanism to adaptively assign scale-specific experts, effectively capturing multi-scale textures while reducing computational redundancy. Furthermore, to prevent the loss of high-frequency details during global abstraction, we introduce a \textbf{Local Spatial Modulation Expert (LSME)} to complement the global modeling, ensuring a precise reconstruction of sharp edges and fine structures. Extensive experiments on standard benchmarks demonstrate that SP-MoMamba achieves superior reconstruction fidelity and a more favorable efficiency-performance trade-off compared to state-of-the-art efficient SR methods.

3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling real-time performance. However, existing methods suffer from a magnitude mismatch in the number of Gaussians generated by image-based and 3DMM-based approaches. This discrepancy results in reconstructed expressions that lack fine-grained detail. In this paper, we introduce a novel method for reconstructing an animatable head avatar from a single image. We propose a Graph splitting network to progressively generate Gaussians from coarse to fine using an autoregressive architecture. To address the graph inconsistency caused by split Gaussians, we employ a mesh topology extension method to align the GNN's connectivity with the increased Gaussian count. Furthermore, we introduce a novel density control method that includes a gating mechanism that generates soft masks for Gaussians, preventing over-densification after the splitting operation. This allows for dynamic control over Gaussian density across different facial regions. For smooth and rapid training, we employ a delayed filtering strategy to avoid re-computing the graph topology during training. Experimental results demonstrate that our autoregressive structure effectively improves expression representation ability by progressively splitting Gaussians. This process, enabled by the GNN-guided splitting, synthesizes more precise facial details and achieves higher reconstruction quality.

Novel view synthesis has been significantly advanced by NeRFs and 3D Gaussian Splatting (3DGS), which require ordering volumetric samples or primitives for correct color blending. While the recent Gaussian-Enhanced Surfels (GES) enable high-performance, sort-free rendering, they suffer from aliasing artifacts and suboptimal reconstruction. To address these limitations, we propose DP-GES, a novel representation that augments opaque surfels with semi-transparent boundaries and leverages Depth Peeling to establish accurate per-pixel ordering. This design enables sort-free Gaussian splatting with correct transmittance modulation, effectively eliminating aliasing and popping artifacts while facilitating a fully differentiable joint optimization. Extensive experiments demonstrate that our method achieves superior reconstruction quality and compares favorably against state-of-the-art techniques across a wide range of scenes.

Validating interpretable surrogate models for ensemble learners requires measuring agreement between the ensemble's internal representation and its surrogate approximation, rather than mere association. Correlation-based approaches are scale-invariant and fail to detect systematic discrepancies in co-occurrence structure. We propose a statistical framework grounded in the agreement-association distinction, centered on the normalized Loss of Interpretability (nLoI). Rooted in the Cressie-Read power divergence family with lambda equal to 2, the nLoI admits a closed-form decomposition into within-node and between-node components, providing a unique diagnostic capability to identify precisely where and why reconstruction fails. The framework incorporates four complementary measures capturing distinct structural facets of approximation quality. A unified permutation testing procedure delivers valid inference for all measures within a single resampling pass. Theoretical properties, including boundedness and symmetry, are established for each metric. Monte Carlo simulations and empirical evaluations confirm exact Type I error control and demonstrate that these measures detect reconstruction fidelity gradients invisible to correlation-based alternatives. The framework is developed and illustrated in the context of Explainable Ensemble Trees (E2Tree), and empirical evaluation on three benchmark datasets illustrates the practical utility of the framework.

Image-to-SVG reconstruction aims to produce vector graphics that are faithful to raster inputs and easy to edit. Existing methods face a structural trade-off in how vector structure is parameterized, including how many paths represent an image and how many anchor points define each path. High-fidelity methods often rely on many paths or densely parameterized curves, whereas overly compact SVG generation may deviate from the input geometry. This issue becomes more pronounced when local raster evidence is imperfect, where boundary-following reconstruction can introduce redundant anchors and fragmented structures. We argue that this trade-off should be addressed at the level of anchor placement, since anchors on Bezier curves define local path structure and strongly affect both accuracy and editability. We propose AnchorFlow, an editable SVG reconstruction framework that models path-level anchor placement with sparse anchor point fields. Given path-like foreground components extracted from a raster image, AnchorFlow predicts an image-conditioned sparse anchor field for each component and resolves it into an ordered Bezier path. Rendering-guided feedback then corrects local structural errors before re-resolution. The recovered paths are then assembled and optimized into the final SVG. Experiments on isolated paths and full images show that AnchorFlow achieves a favorable fidelity-editability trade-off, substantially reducing editable complexity while preserving competitive raster fidelity.

Assessing the quality of single image super-resolution (SISR) results remains an open methodological problem. Common full-reference metrics (PSNR, SSIM, LPIPS) do not explicitly evaluate the preservation of the geometric structure of images, which is critical for the correctness of scale-based reconstruction. In addition, they require the forced alignment of images to the same size (\textit{forced resizing}), which introduces an external interpolation error into the evaluation process. This paper proposes a diagnostic scale-invariant quality measure, MSIQ (\textit{Moment-based Scale-Invariant Quality}), based on the comparison of normalized central geometric moments of two images. MSIQ enables direct comparison of images with different spatial resolutions without resizing, is mathematically deterministic (\textit{model-free}), and has an analytical form. To provide a theoretical basis for the approach, we introduce a conceptual distinction between the ability of metrics to monotonically track degradation (\textit{tracking ability}) and their geometric selectivity (\textit{geometric specificity}). The experimental validation confirmed the stability of MSIQ under uniform scaling and, at the same time, revealed the high sensitivity of traditional metrics to the choice of interpolation method. The results show that MSIQ has pronounced geometric selectivity: the proposed measure effectively separates geometric deformations from non-geometric artifacts, in particular JPEG compression, unlike pixel-based and perceptual metrics. It is also shown that the response of MSIQ to structural perturbations remains stable across different classes of SR algorithms, including DNN models with different architectures. The proposed measure is a complementary diagnostic tool for domains where geometric fidelity has priority, in particular medical imaging and remote sensing.

We present ForMaT (Format-Preserving Multilingual Translation), a parallel corpus of 3,956 PDFs across 15 language pairs that preserves original layout metadata proposed for multimodal machine translation. To ensure structural diversity in the dataset, we employ K-Medoids sampling over 45 geometric features, capturing complex elements like nested tables and formulas to focus only on visually diverse PDF documents. Our evaluation reveals that current MT systems struggle with spatial grounding and geometric synchronization, often losing the link between text and its visual context. ForMaT provides a benchmark for developing layout-aware translation models that integrate visual and textual context for high-fidelity document reconstruction.

Recent generative methods for single-shot high dynamic range (HDR) image reconstruction show promising results, but often struggle with preserving fidelity to the input image. They require separate models to handle highlights and shadows, or sacrifice interpretability by directly predicting the final HDR image. We address these limitations by re-casting single-shot HDR reconstruction as conditional video generation and fusing the generated frames into an HDR image. We finetune a video diffusion model to generate an exposure bracket, conditioned on a low dynamic range (LDR) input. We fuse this image bracket using per-pixel weights predicted by a light-weight UNet. This formulation is simple, interpretable, and effective. Rather than directly hallucinating an HDR image, it explicitly reconstructs the intermediate exposure stack and fuses it into the final output. Our method eliminates the need for separate models across exposure regimes and produces HDR reconstructions with high input fidelity. On quantitative benchmarks, we outperform state-of-the-art generative baselines with comparable model capacity on several reconstruction metrics. Human evaluators further prefer our results in 72% of pairwise comparisons against existing methods. Finally, we show that this input-conditioned sequence generation and fusion framework extends beyond HDR to other image reconstruction tasks, such as all-in-focus image recovery from a single defocus-blurred input.

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to $256 \times 256$. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a $12\times$ inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by $23.1\%$ in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.

Recent frameworks like ToFu and TEMPEH provide an automated alternative to classical registration pipelines by predicting 3D meshes in dense semantic correspondence directly from calibrated multi-view images. However, these learning-based methods rely on the slow, manual registration pipelines they aim to replace for their training supervision. We overcome this limitation with MOCHI (Multi-view Optimizable Correspondence of Heads from Images), a multi-view 3D face prediction framework trained without requiring registered training data. MOCHI eliminates the registration data dependency by enforcing topological consistency through a pseudo-linear inverse kinematic solver. Semantic alignment is guided by dense keypoints from a 2D landmark predictor trained exclusively on synthetic data. Our analysis further reveals that standard point-to-surface distances induce training instabilities and visual artifacts in registration-free settings. We propose pointmap- and normal-based losses instead, which provide smoother gradients and superior reconstruction fidelity. Finally, we introduce a test-time optimization scheme that refines network weights over a few dozen iterations. This approach bridges the gap between feed-forward efficiency and iterative optimization precision, allowing MOCHI to outperform traditional labor-intensive pipelines in both reconstruction accuracy and visual quality. Code and model are public at: https://filby89.github.io/mochi.

Scalable compression is essential for bandwidth-adaptive transmission, yet most learned codecs are optimized for a fixed rate-distortion point, making rate adaptation costly due to re-encoding or maintaining multiple bitstreams. In this work, we propose TAFA-GSGC, a scalable learned point cloud geometry codec that enables multi-quality decoding from a single bitstream and a single trained model. TAFA-GSGC combines layered residual refinement with channel-group entropy coding, and introduces a Target-Aligned Feature Aggregation module to reduce cross-layer redundancy in enhancement residuals. Our framework supports up to 9 decodable quality levels with monotonic quality improvement as more subbitstreams are received, while maintaining strong compression efficiency. Compared with the PCGCv2 baseline, TAFA-GSGC demonstrates improved RD performance, achieving average BD-rate reductions of 4.99% and 5.92% in terms of D1-PSNR and D2-PSNR, respectively.

Egocentric video provides a unique view into human perception and interaction, with growing relevance for augmented reality, robotics, and assistive technologies. However, rapid camera motion and complex scene dynamics pose major challenges for 3D reconstruction from this perspective. While 3D Gaussian Splatting (3DGS) has become a state-of-the-art method for efficient, high-quality novel view synthesis, variants, that focus on reconstructing dynamic scenes from monocular video are rarely evaluated on egocentric video. It remains unclear whether existing models generalize to this setting or if egocentric-specific solutions are needed. In this work, we evaluate dynamic monocular 3DGS models on egocentric and exocentric video using paired ego-exo recordings from the EgoExo4D dataset. We find that reconstruction quality is consistently lower in egocentric views. Analysis reveals that the difference in reconstruction quality, measured in peak signal-to-noise ratio, stems from the reconstruction of static, not dynamic, content. Our findings underscore current limitations and motivate the development of egocentric-specific approaches, while also highlighting the value of separately evaluating static and dynamic regions of a video.

Large-scale kernel ridge regression (KRR) is limited by the need to store a large kernel matrix K_t. To avoid storing the entire matrix K_t, Nystrom methods subsample a subset of columns of the kernel matrix, and efficiently find an approximate KRR solution on the reconstructed matrix. The chosen subsampling distribution in turn affects the statistical and computational tradeoffs. For KRR problems, recent works show that a sampling distribution proportional to the ridge leverage scores (RLSs) provides strong reconstruction guarantees for the approximation. While exact RLSs are as difficult to compute as a KRR solution, we may be able to approximate them well enough. In this paper, we study KRR problems in a sequential setting and introduce the INK-ESTIMATE algorithm, that incrementally computes the RLSs estimates. INK-ESTIMATE maintains a small sketch of K_t, that at each step is used to compute an intermediate estimate of the RLSs. First, our sketch update does not require access to previously seen columns, and therefore a single pass over the kernel matrix is sufficient. Second, the algorithm requires a fixed, small space budget to run dependent only on the effective dimension of the kernel matrix. Finally, our sketch provides strong approximation guarantees on the distance between the true kernel matrix and its approximation, and on the statistical risk of the approximate KRR solution at any time, because all our guarantees hold at any intermediate step.

Reconstructing dense 3D geometry from continuous video streams requires stable inference under a constant memory budget. Existing $O(1)$ frameworks primarily rely on a ``pure eviction'' paradigm, which suffers from significant information destruction due to binary token deletion and evaluation noise from localized, single-layer scoring. To address these bottlenecks, we propose StreamCacheVGGT, a training-free framework that reimagines cache management through two synergistic modules: Cross-Layer Consistency-Enhanced Scoring (CLCES) and Hybrid Cache Compression (HCC). CLCES mitigates activation noise by tracking token importance trajectories across the Transformer hierarchy, employing order-statistical analysis to identify sustained geometric salience. Leveraging these robust scores, HCC transcends simple eviction by introducing a three-tier triage strategy that merges moderately important tokens into retained anchors via nearest-neighbor assignment on the key-vector manifold. This approach preserves essential geometric context that would otherwise be lost. Extensive evaluations on five benchmarks (7-Scenes, NRGBD, ETH3D, Bonn, and KITTI) demonstrate that StreamCacheVGGT sets a new state-of-the-art, delivering superior reconstruction accuracy and long-term stability while strictly adhering to constant-cost constraints.

Anchor-driven 4D Gaussian streaming methods such as Instant Gaussian Stream (IGS) update a dynamic scene each frame from a compact set of Gaussian anchors, chosen by default with Farthest Point Sampling (FPS) at a fixed budget of $8{,}192$. Because these anchors act as control points that drive the whole scene through linear blend skinning, the rule used to choose them ought to affect reconstruction quality. We test this by holding the IGS pipeline fixed and changing only the sampler, comparing FPS, random, uniform, an opacity-scale heuristic, and a learned policy across budgets and refinement settings on N3DV and MeetingRoom. At deployment budgets the sampler has no measurable effect: a cheap random or uniform sampler at $4{,}096$ anchors matches FPS@8192 within measurement error, the default budget is over-provisioned, and the result holds on a second backbone (3DGStream). The learned policy is mixed rather than consistently better: it can improve the N3DV validation set at tight budgets, but does not give a stable cross-dataset rule, and selection is never the bottleneck because refinement dominates runtime. We will release our full sweep and evaluation protocol as a sampler benchmark.

Extracting an explicit surface that exactly matches the zero-level set of a neural signed distance function (SDF) remains challenging. Sampling-based isosurfacing methods such as Marching Cubes introduce discretization error. In contrast, continuous piecewise affine (CPWA) analytic approaches typically require plain ReLU MLPs, which limits the ability to learn high-frequency SDFs in practice. We present TetraSDF, an analytic isosurface extraction framework for SDFs that retains the expressiveness of grid-based encoders while enabling exact zero-level set extraction, by representing the SDF with a ReLU MLP composed with a multi-resolution tetrahedral positional encoder. Our positional encoder's barycentric interpolation preserves a global CPWA structure, allowing us to track ReLU linear regions within an encoder-induced polyhedral complex. We further introduce a fixed analytic input preconditioner derived from the encoder's metric to reduce directional bias, thereby stabilizing training. Across multiple benchmarks, TetraSDF matches or surpasses existing grid-based encoders in SDF reconstruction accuracy, while faithfully recovering the network's zero-level set as a triangle mesh.

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.