Fast compressed sensing recovery using generative models and sparse deviations modeling

This paper develops an algorithm to effectively explore the advantages of both sparse vector recovery methods and generative model-based recovery methods for solving compressed sensing recovery problem. The proposed algorithm mainly consists of two steps. In the first step, a network-based projected gradient descent (NPGD) is introduced to solve a non-convex optimization problem, obtaining a preliminary recovery of the original signal. Then with the obtained preliminary recovery, a l1 norm regularized optimization problem is solved by optimizing for sparse deviation vectors. Experimental results on two bench-mark datasets for image compressed sensing clearly demonstrate that the proposed recovery algorithm can bring about high computation speed, while decreasing the reconstruction error continuously with increasing the number of measurements.