# Group-based Sparse Representation for Image Restoration

arXiv: https://arxiv.org/abs/1405.3351 · HTML: https://mlsanity.com/paper/1405.3351/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2014.

## Built on by (most cited first, 30 of 39)

- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Dynamic Attentive Graph Learning for Image Restoration](https://mlsanity.com/paper/2109.06620/) (2021)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [COLA-Net: Collaborative Attention Network for Image Restoration](https://mlsanity.com/paper/2103.05961/) (2021)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [TransCL: Transformer Makes Strong and Flexible Compressive Learning](https://mlsanity.com/paper/2207.11972/) (2022)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Global Sensing and Measurements Reuse for Image Compressed Sensing](https://mlsanity.com/paper/2206.11629/) (2022)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [Dual-Scale Transformer for Large-Scale Single-Pixel Imaging](https://mlsanity.com/paper/2404.05001/) (2024)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)
- [Deep Unfolding Network for Image Compressed Sensing by Content-adaptive Gradient Updating and Deformation-invariant Non-local Modeling](https://mlsanity.com/paper/2310.10033/) (2023)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Alternative Learning Paradigms for Image Quality Transfer](https://mlsanity.com/paper/2411.05885/) (2024)
- [MB-RACS: Measurement-Bounds-based Rate-Adaptive Image Compressed Sensing Network](https://mlsanity.com/paper/2402.16855/) (2024)
- [Deep Network for Image Compressed Sensing Coding Using Local Structural Sampling](https://mlsanity.com/paper/2402.19111/) (2024)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Quantized Proximal Averaging Network for Analysis Sparse Coding](https://mlsanity.com/paper/2105.06211/) (2021)
- [ATP-Net: An Attention-based Ternary Projection Network For Compressed Sensing](https://mlsanity.com/paper/2106.12728/) (2021)
- [A Fast Alternating Minimization Algorithm for Coded Aperture Snapshot Spectral Imaging Based on Sparsity and Deep Image Priors](https://mlsanity.com/paper/2206.05647/) (2022)
- [Group Sparse Coding for Image Denoising](https://mlsanity.com/paper/2212.11501/) (2022)
- [Region-wise matching for image inpainting based on adaptive weighted low-rank decomposition](https://mlsanity.com/paper/2303.12421/) (2023)

## Abstract (arXiv)

Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal patches with similar structures, and establish a novel sparse representation modeling of natural images, called group-based sparse representation (GSR). The proposed GSR is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. Moreover, an effective self-adaptive dictionary learning method for each group with low complexity is designed, rather than dictionary learning from natural images. To make GSR tractable and robust, a split Bregman based technique is developed to solve the proposed GSR-driven minimization problem for image restoration efficiently. Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both PSNR and visual perception.