Image Deblurring

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this problem, both the point spread function (PSF) and the underlying latent sharp image must be estimated simultaneously. This problem cannot be solved directly due to its ill-posed nature. One powerful tool for solving such problems is total variation (TV) regularization. The $\ell_0$-norm regularization within the TV framework has been widely adopted to promote sparsity in image gradients or transform domains, leading to improved preservation of edges and fine structures. However, the use of the $\ell_0$-norm results in a highly nonconvex and computationally intractable optimization problem, which limits its practical applicability. To overcome these difficulties, we employ the minimax concave penalty (MCP), which promotes enhanced sparsity and provides a closer approximation to the $\ell_0$-norm. In addition, a reweighted $\ell_1$-norm regularization is incorporated to further reduce estimation bias and improve the preservation of fine image details and textures. After introducing the proposed model, a numerical algorithm is developed to solve the resulting optimization problem. The effectiveness of the proposed approach is then demonstrated through experimental evaluations on several test images.

This paper presents a novel saturation aware space variant blind image deblurring framework designed to address challenges posed by saturated pixels in deblurring under high dynamic range and low light conditions. The proposed approach effectively segments the image based on blur intensity and proximity to saturation, leveraging a pre estimated Light Spread Function to mitigate stray light effects. By accurately estimating the true radiance of saturated regions using the dark channel prior, our method enhances the deblurring process without introducing artifacts like ringing. Experimental evaluations on both synthetic and real world datasets demonstrate that the framework improves deblurring outcomes across various scenarios showcasing superior performance compared to state of the art saturation-aware and general purpose methods. This adaptability highlights the framework potential integration with existing and emerging blind image deblurring techniques.

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In applications such as blind deblurring, this principle is used to recover sharp images from degraded observations. In this paper, we analyze the recovery guarantees of MAP-based methods by adopting a \emph{Morse--Bott framework}. We model the image potential as a Morse--Bott function, where natural images are modeled as residing locally on a critical submanifold. This means that while the potential is locally flat along the natural'' directions of the image manifold, it is strictly convex in the directions normal to it. We demonstrate that this Morse--Bott hypothesis aligns with the structural properties of state-of-the-art learned priors, a finding we validate through an experimental analysis of the potential landscape and its Hessian spectrum. Our theoretical results show that, in a neighborhood of the ground-truth image and operator, the posterior admits local minimizers that are stable both with respect to initialization (gradient descents converge to the same minimizer) and to small perturbations of the data (solutions vary smoothly with the observations). This local stability potentially provides a theoretical justification for the empirical success of well designed gradient-based optimization in these settings. However, we also demonstrate that this local stability is a \textbf{local} property: the blurry trap'', well-known for sparse priors in blind deconvolution, persists even with state-of-the-art learned priors. Our findings demonstrate that the failure of MAP in blind deconvolution is not a limitation of prior quality, but an intrinsic characteristic of the landscape. We conclude that successful recovery depends on strategic initialization around favorable local minima.

Motion blur remains one of the most common and visually disruptive degradations in real-world smartphone imaging, yet existing deblurring benchmarks are often limited in scale, resolution, or domain relevance. This gap is especially pronounced for smartphones, where rolling shutter, small sensors, and ISP processing produce blur statistics that differ from GoPro/DSLR-based benchmarks. We introduce a large-scale smartphone-oriented deblurring dataset constructed from 240~fps slow-motion video. To approximate exposure-time radiance integration, we synthesize blur by temporally averaging a fixed window of $N=30$ consecutive frames, which corresponds to an effective exposure of $T=1/8$~second, and we select the temporally centered frame as the sharp ground truth. The resulting benchmark contains 42,045 paired blur--sharp images at $1920\times1080$ resolution spanning 843 distinct scenes, with a train/test split of 37,841/4,204 pairs. We benchmark multiple state-of-the-art deblurring models using PSNR and SSIM and observe consistent performance degradation relative to the baseline similarity between the input blurry images and ground truth, underscoring the realism and difficulty of the proposed data. We release the dataset and generation scripts via HuggingFace to facilitate the development and evaluation of robust, deployment-oriented deblurring methods.

The Transformer architecture has achieved remarkable success in natural language processing and high-level vision tasks over the past few years. However, the inherent complexity of self-attention is quadratic to the size of the image, leading to unaffordable computational costs for high-resolution vision tasks. In this paper, we introduce Concertormer, featuring a novel Concerto Self-Attention (CSA) mechanism designed for image deblurring. The proposed CSA divides self-attention into two distinct components: one emphasizes generally global and another concentrates on specifically local correspondence. By retaining partial information in additional dimensions independent from the self-attention calculations, our method effectively captures global contextual representations with complexity linear to the image size. To effectively leverage the additional dimensions, we present a Cross-Dimensional Communication module, which linearly combines attention maps and thus enhances expressiveness. Moreover, we amalgamate the two-staged Transformer design into a single stage using the proposed gated-dconv MLP architecture. While our primary objective is single-image motion deblurring, extensive quantitative and qualitative evaluations demonstrate that our approach performs favorably against the state-of-the-art methods in other tasks, such as deraining and deblurring with JPEG artifacts. The source codes and trained models will be made available to the public.