Stable and Lightweight Deep Primal-Dual Unrolling for Constrained Image Restoration with Convolutional Sparse Coding

This paper proposes an image restoration method using a convolutional sparse coding (CSC) unrolling network with a box constraint and total variation. Unlike conventional deep unrolling methods, the proposed method constructs an interpretable lightweight network with restoration stability. Specifically, we design a new constrained convex optimization problem that incorporates CSC, a box constraint, and total variation (TV). The box constraint ensures that the image values fall within a certain range, making the restoration process stable. In addition, combining total variation and CSC leads to high interpretability and representation with a small number of parameters. We develop an optimization algorithm based on the primal-dual splitting (PDS) method. Then, by unrolling the algorithm, we construct the proposed lightweight network. Experimental results demonstrate the superiority of the proposed method in image restoration accuracy and lightweightness of the proposed network in the number of parameters.