Image Deblurring

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 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 **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.