Convolutional Sparse Coding with Weighted L1 Norm for Phase Retrieval: Algorithm and Its Deep Unfolded Network

Recovering the image of interest from its phaseless measurement is the goal of phase retrieval (PR). Recent PR algorithms that use hand-crafted priors suffer from low-quality reconstructions. To cope with this limitation, we exploit structural priors to propose a novel deep unfolded convolutional sparse coding phase retrieval network. Firstly, we formulate a weighted ℓ 1 norm (WL1) minimization problem utilizing convolutional sparse coding for PR, and solve it by using an iterative algorithm. An inertial epigraph method employing the inertial technique is proposed to solve the PR subproblem. Secondly, differing from updating weights of WL1 by using a fixed inverse proportional function in traditional methods, we learn such a function that can determine these crucial weights via a deep convolutional neural network equipped with the attention mechanism. Finally, we unroll the iterative PR algorithm to build a deep feedforward network architecture. Experiments demonstrate that the resulting model-based deep network can recover higherquality images, compared with the existing PR algorithms at various noise levels. The testing data and codes are published at https://github.com/shibaoshun/PRNet.