Accelerating L1-L1 convolutional sparse coding through primal-dual Douglas-Rachford splitting

Convolutional sparse coding (CSC) reconstructs a signal using given spatial patterns by identifying their sparse distributions through a convex optimization, achieving notable success in image processing applications. This paper proposes solving the recently proposed L1-L1 CSC by applying primal-dual Douglas-Rachford (DR) splitting, which can converge faster than the traditionally applied Alternating Direction Method of Multipliers (ADMM). The proposed CSC demonstrated comparable convergence under an intuitive hyperparameter setting, verifying the correctness of our formulation and suggesting the potential for convergence acceleration with optimal settings.