Deep Unfolding

This study explores the combination of automated machine learning (AutoML) with model-based deep unfolding (DU) for optimizing wireless beamforming and waveforms. We convert the iterative proximal gradient descent (PGD) algorithm into a deep neural network, wherein the parameters of each layer are learned instead of being predetermined. Additionally, we enhance the architecture by incorporating a hybrid layer that performs a learnable linear gradient transformation prior to the proximal projection. By utilizing AutoGluon with a tree-structured parzen estimator (TPE) for hyperparameter optimization (HPO) across an expanded search space, which includes network depth, step-size initialization, optimizer, learning rate scheduler, layer type, and post-gradient activation, the proposed auto-unrolled PGD (Auto-PGD) achieves 98.8% of the spectral efficiency of a traditional 200-iteration PGD solver using only five unrolled layers, while requiring only 100 training samples. We also address a gradient normalization issue to ensure consistent performance during training and evaluation, and we illustrate per-layer sum-rate logging as a tool for transparency. These contributions highlight a notable reduction in the amount of training data and inference cost required, while maintaining high interpretability compared to conventional black-box architectures.

Existing computational spectral imaging systems typically rely on coded aperture and beam splitters that block a substantial fraction of incident light, degrading reconstruction quality under light-starved conditions. To address this limitation, we develop the Oscillating Dispersion Imaging Spectrometer (ODIS), which for the first time achieves near-full light throughput by axially translating a disperser between the conjugate image plane and a defocused position, sequentially capturing a panchromatic (PAN) image and a dispersed measurement along a single optical path. We further propose a PAN-guided Dispersion-Aware Deep Unfolding Network (PDAUN) that recovers high-fidelity spectral information from maskless dispersion under PAN structural guidance. Its data-fidelity step derives an FFT-Woodbury preconditioned solver by exploiting the cyclic-convolution property of the ODIS forward model, while a Dispersion-Aware Deformable Convolution module (DADC) corrects sub-pixel spectral misalignment using PAN features. Experiments show state-of-the-art performance on standard benchmarks, and cross-system comparisons confirm that ODIS yields decisive gains under low illumination. High-fidelity reconstruction is validated on a physical prototype.

Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs), variational auto-encoders and normalising flows offer a computationally efficient alternative for posterior sampling. However, push-forward models are opaque as they lack the modularity of Bayes Theorem, leading to poor generalisation with respect to changes in the likelihood function. In this work, we introduce a novel approach to GAN architecture design by applying deep unfolding to Langevin MCMC algorithms. This paradigm maps fixed-step iterative algorithms onto modular neural networks, yielding architectures that are both flexible and amenable to interpretation. Crucially, our design allows key model parameters to be specified at inference time, offering robustness to changes in the likelihood parameters. We train these unfolded samplers end-to-end using a supervised regularized Wasserstein GAN framework for posterior sampling. Through extensive Bayesian imaging experiments, we demonstrate that our proposed approach achieves high sampling accuracy and excellent computational efficiency, while retaining the physics consistency, adaptability and interpretability of classical MCMC strategies.

Deep unfolding networks (DUNs), combining conventional iterative optimization algorithms and deep neural networks into a multi-stage framework, have achieved remarkable accomplishments in Image Restoration (IR), such as spectral imaging reconstruction, compressive sensing and super-resolution.It unfolds the iterative optimization steps into a stack of sequentially linked blocks.Each block consists of a Gradient Descent Module (GDM) and a Proximal Mapping Module (PMM) which is equivalent to a denoiser from a Bayesian perspective, operating on Gaussian noise with a known level.However, existing DUNs suffer from two critical limitations: (i) their PMMs share identical architectures and denoising objectives across stages, ignoring the need for stage-specific adaptation to varying noise levels; and (ii) their chain of structurally repetitive blocks results in severe parameter redundancy and high memory consumption, hindering deployment in large-scale or resource-constrained scenarios.To address these challenges, we introduce generalized Deep Low-rank Adaptation (LoRA) Unfolding Networks for image restoration, named LoRun, harmonizing denoising objectives and adapting different denoising levels between stages with compressed memory usage for more efficient DUN.LoRun introduces a novel paradigm where a single pretrained base denoiser is shared across all stages, while lightweight, stage-specific LoRA adapters are injected into the PMMs to dynamically modulate denoising behavior according to the noise level at each unfolding step.This design decouples the core restoration capability from task-specific adaptation, enabling precise control over denoising intensity without duplicating full network parameters and achieving up to $N$ times parameter reduction for an $N$-stage DUN with on-par or better performance.Extensive experiments conducted on three IR tasks validate the efficiency of our method.

Reconstructing a three-dimensional hyperspectral cube from a two-dimensional compressed measurement is a severely ill-posed inverse problem. Existing deep unfolding networks (DUNs) retain fidelity to the imaging model, but regression-trained denoisers can suppress spatial detail and smooth spectral structure under strong modulation. This paper proposes FMU, a deep unfolding framework that couples a measurement-conditioned flow-matching prior with a sensing-model-guided measurement update. A two-phase scheme first learns a compact clean-HSI latent target and then trains a conditional velocity field to generate this target from Gaussian noise. A mean-velocity regularizer additionally penalizes the first-moment error of the learned field. On the KAIST 10-scene benchmark under the optical-filter setting, FMU obtains 42.13,dB PSNR and 0.9900 SSIM, outperforming LADE-DUN by 1.16,dB in PSNR under the same training data, sensing mask, and evaluation protocol. Under the same optical-filter operator, FMU is further evaluated on held-out KAIST and ICVL scenes without fine-tuning. We also report quantitative simulated-CASSI results and qualitative reconstructions of real CASSI measurements.

Humans learn in two complementary ways: a slow, cumulative process that builds broad, general knowledge, and a fast, on-the-fly process that captures specific experiences. Existing deep-unfolding methods for spectral compressive imaging (SCI) mirror only the slow component-relying on heavy pre-training with many unfolding stages-yet they lack the rapid adaptation needed to handle new optical configurations. As a result, they falter on out-of-distribution cameras, especially in bespoke spectral setups unseen during training. This depth also incurs heavy computation and slow inference. To bridge this gap, we introduce SlowFast-SCI, a dual-speed framework seamlessly integrated into any deep unfolding network beyond SCI systems. During slow learning, we pre-train or reuse a priors-based backbone and distill it via imaging guidance into a compact fast-unfolding model. In the fast learning stage, lightweight adaptation modules are embedded within each stage and fine-turned self-supervised at test time via a self-supervised loss-without retraining the backbone. To the best of our knowledge, SlowFast-SCI is the first testtime adaptation-driven deep unfolding framework for efficient, self-adaptive spectral reconstruction. Its dual-stage design unites offline robustness with on-the-fly per-sample calibration-yielding over 70% reduction in parameters and FLOPs, up to 5.79 dB PSNR improvement on out-of-distribution data, preserved cross-domain adaptability, and a 4x faster adaptation speed. In addition, its modularity integrates with any deep-unfolding network, paving the way for self-adaptive, field-deployable imaging and expanded computational imaging modalities. Code is available in Supplementary Material. The models, datasets, and code are available at https://github.com/XuanLu11/SlowFast-SCI.

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_{L}$, where $\mathcal{F}^{(p)}_{l}$ is a family of functions spanned by a B-spline basis function of order $p$ at a chosen scale and its integer shifts. The projected low-pass coefficients $F_l^*$ are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting $\ell_1$-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.