Proximal-Gen for fast compressed sensing recovery

Abstract Compressed sensing (CS) can recover an image from a few random measurements by exploiting the sparsity assumption on the structure of images. Some recent generative model-based CS recovery methods have removed the sparsity constraint, but their recovery process is slow and the recovered signal is constrained to be in the generator range. Here, we propose a new framework, called Proximal-Gen, for CS recovery. Specifically, we first formulate a general domain of the recovered signals, this allows the subsequent recovery algorithms to recover the signals that deviate from the generator range. Then based on the general domain, we develop a fast recovery algorithm, which mainly consists of two sub-algorithms, namely network-based projected gradient descent (NPGD) and denoiser-based proximal gradient descent (DPGD). The NPGD is used to obtain an intermediate signal lying in the generator range, while the DPGD is proposed to recover a deviation signal. Compared with multiple recent generative model-based recovery methods, our method can achieve better reconstruction performance and higher efficiency under most measurements.