Group-Based Sparse Representation for Image Restoration

By Jian Zhang, Debin Zhao, Wen Gao. IEEE Transactions on Image Processing, 2014

730 citations recorded by the source corpus.

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. In addition, 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 ℓ0 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 peak signal-to-noise ratio and visual perception.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/5dc7b5f64d1f2bc8cbed4f0273bf873eb38d6a23

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Chong Mou
2. Jian Zhang
3. Qian Wang
4. David J. Brady
5. Xin Yuan
6. Bernard Ghanem
7. J. Suo
8. Qionghai Dai

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Lei Zhang
3. Dacheng Tao
4. Jian Yang
5. Bernard Ghanem
6. Xuelong Li
7. Leyuan Fang
8. Yong Xu

Citations in the corpus

• A Survey of Sparse Representation: Algorithms and Applications (2015, background): “[180] proposed a groupbased sparse representation, which combined characterist i s from local sparsity and nonlocal self-similarity of natura l images to the domain of the group.”
• Deep Generalized Unfolding Networks for Image Restoration (2022, methodology): “As mentioned previously, model-based methods [85, 87, 98, 99] usually solve IR in a Bayesian perspective, which is formulated into a MAP optimization problem as Eq.”
• Rank Minimization for Snapshot Compressive Imaging (2018, background): “Invoking the law of large numbers in probability theory, we have the following equation with a very large probability (limited to 1) at each iteration [50], i.e. , ∀ ε > 0 , lim The proof can be found in [51].”
• Image Compressed Sensing Using Convolutional Neural Network (2020, methodology): “Different with previous BCS [24], [25], the matrix ̃B in CSNet is optimized adaptively in a network instead of the pseudo-inverse matrix of B .”
• ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing (2017, methodology): “ploiting the non-local self-similarity properties of natural images have been proposed to improve CS reconstruction [48, 46, 10, 52].”
• Hyperspectral Image Super-Resolution via Non-local Sparse Tensor Factorization (2017, background): “These non-local similar patches are often clustered together before processing, which can be exploited to enhance the performance of image denoising [39] and demosaicking [18].”