A Variational Bayesian Inference-Inspired Unrolled Deep Network for Compressed Sensing

Deep learning (DL)-based algorithms were recently developed for compressed sensing. Specifically, a class of deep unfolding-based methods have gained much attention due to their ability of integrating the power of learning with the algorithmic structure. Nevertheless, most of these deep unfolding-based methods still require a large number of learnable parameters. In this paper, we develop an unrolled deep network for compressed sensing within an inverse-free variational Bayesian framework. Compared with existing networks, the proposed unrolled deep network has substantially fewer learnable parameters. The proposed network can therefore achieve better recovery performance with fewer training samples. This makes it useful for scenarios where training samples are costly to be acquired.