DeepGSR: Deep Group-Based Sparse Representation Network for Solving Image Inverse Problems

In the past few years, group-based sparse representation (GSR) has emerged as a powerful paradigm for image inverse problems by synergizing model-driven interpretability with nonlocal self-similarity priors. Nevertheless, its practical utility is hindered by computationally expensive iterative processes. Deep learning (DL) methods can avoid this deficiency, but they often lack of model interpretability. To bridge this gap, we propose a novel deep group-based sparse representation framework, termed DeepGSR, which brings the GSR method and the DL approach together. DeepGSR not only circumvents the iterative bottlenecks of conventional GSR but also preserves its model interpretability through a learnable parameterization. Specifically, the network is built upon a GSR model that leverages nonlocal self-similarity, and it integrates adaptive patch matching and aggregation mechanisms to model complex intra-group relationships in the latent space. To reduce the computational complexity associated with traditional SVD-based rank shrinkage, we introduce a learnable low-rank shrinkage module that incorporates low-rank constraints while enhancing the interpretability and adaptability of the model. To better exploit frequency-specific structures, the network incorporates a shifting wavelet-domain patch partitioning strategy, which separately models high- and low-frequency components to further enhance the representation ability of the network. Extensive experiments demonstrate that DeepGSR, when applied as a drop-in replacement module to various image inverse problems such as image denoising, single-image deraining, metal artifact reduction, sparse-view computed tomography reconstruction, phase retrieval, and all-in-one image restoration consistently delivers effective performance, validating the effectiveness of the proposed framework. The source code and datasets have been made publicly available at https://github.com/shibaoshun/DeepGSR.