Unfolding Convolutional Sparse Coding With Low-rank-Guided Hybrid Priors for Image Denoising

Image denoising remains a challenging problem due to the ill-posed nature of recovering clean images from noisy observations. Prior-based modeling plays a vital role in addressing this challenge. Low-rank priors effectively exploit non-local self-similarity by modeling correlations across similar images, but often over-smooth fine textures. In contrast, sparse priors, especially in the form of Convolutional Sparse Coding (CSC), excel at preserving high-frequency texture details, yet typically neglect the structure across images. Recent unfolded CSC networks have improved denoising performance by combining CSC with deep networks, but most of them rely solely on sparsity, overlooking the complementary low-rank structure information. To overcome these limitations, we propose UCSC-LR, the first interpretable unfolded CSC network that jointly leverages both sparse and low-rank priors within a unified architecture. UCSC-LR unrolls both the Iterative Shrinkage-Thresholding Algorithm (ISTA) and Singular Value Thresholding (SVT) to strictly implement alternating minimization, enabling simultaneous pursuit of sparse representations and low-rank reconstructions. A dedicated Fusion Net is introduced to adaptively integrate features from the two priors, allowing the model to preserve both texture and structural content. To further enhance performance on color image denoising, UCSC-LR incorporates a lightweight channel attention mechanism to capture inter-channel dependencies. With shared, pre-learned convolutional dictionaries and efficient parameterization, UCSC-LR achieves state-of-the-art performance with low model complexity. Extensive experiments on grayscale, blind, and color denoising tasks validate the effectiveness of the proposed method, consistently surpassing existing CSC-based and deep learning-based denoisers.