Adaptive Use of Convex or Non-Convex Optimization in Deep Unfolding Network for Image Compressive Sensing

Recently, deep unfolding networks (DUNs) have emerged as a promising technique for image Compressive Sensing (CS) reconstruction by unfolding optimization algorithms, where each stage of the DUNs corresponds to an iteration of the optimization algorithm. DUNs can be divided into convex optimization based methods and non-convex optimization based methods. On the one hand, DUNs based on convex optimization algorithms cannot handle non-convex optimization problems, thereby limiting their use when the prior term is a non-convex function. On the other hand, although DUNs based on non-convex optimization algorithms can handle more complex prior terms to make global optimal solutions closer to the ground truth, there is a high probability that they converge only to a local optimum. Therefore, in practical applications, it is necessary to consider the various characteristics of the problem comprehensively, then design appropriate prior terms and choose convex or non-convex optimization in DUN. This paper proposes ViP-DUN method to learn suitable prior terms and adaptively use convex or non-convex optimization. ViP-DUN learns deep prior terms and variable metrics in a data-driven manner to achieve adaptive use of convex or non-convex optimization. Moreover, we designed a lightweight multi-scale information fusion module in ViP-DUN at the network structure level to further enhance the network's processing capability. Experiments demonstrate that our proposed method can improve image reconstruction quality at multiple compression rates through the adaptive capabilities of the network. Our complete code will be made publicly available upon acceptance.