G2-DUN: Gradient Guided Deep Unfolding Network for Image Compressive Sensing

Inspired by certain optimization solvers, the deep unfolding network (DUN) usually inherits a multi-phase structure for image compressive sensing (CS). However, in existing DUNs, the message transmission within and between phases still faces two issues: 1) the roughness of transmitted information, e.g., the low-dimensional representations. 2) the inefficiency of transmitted policy, e.g., simply concatenating deep features. In this paper, by unfolding the Proximal Gradient Descent (PGD) algorithm, a novel gradient guided DUN (G2 -DUN) for image CS is proposed, in which a gradient map is delicately introduced within each phase for providing richer informational guidance at both intra-phase and inter-phase levels. Specifically, corresponding to the gradient descent (GD) of PGD, a gradient guided GD module is designed, in which the gradient map can adaptively guide step size allocation for different textures of input image, realizing a content-aware gradient updating. On the other hand, corresponding to the proximal mapping (PM) of PGD, a gradient guided PM module is developed, in which the gradient map can dynamically guide the exploring of deep textural priors in multi-scale space, achieving the dynamic perception of the proposed deep model. By introducing the gradient map, the proposed message transmission system not only facilitates the informational communication between different functional modules within each phase, but also strengthens the inferential cooperation among cascaded phases. Extensive experiments manifest that the proposed G2 -DUN outperforms existing state-of-the-art CS methods.