Learning Non-Locally Regularized Compressed Sensing Network With Half-Quadratic Splitting

Deep learning-based Compressed Sensing (CS) reconstruction attracts much attention in recent years, due to its significant superiority of reconstruction quality. Its success is mainly attributed to the employment of a large dataset for pre-training the network to learn a reconstruction mapping. In this paper, we propose a non-locally regularized compressed sensing network for reconstructing image sequences, which can achieve high reconstruction quality without pre-training. Specifically, the proposed method attempts to learn a deep network prior for the reconstruction of an individual instance under the constraint that the network output can well match the given CS measurement. The non-local prior is designed to guide the network to capture the long-range dependencies by exploiting the self-similarities among images, and it can also make the network noise-aware. In order to deal with the compound of non-local prior and deep network prior, we construct a half-quadratic splitting based optimization method for network learning, in which the two priors are decoupled into two simple sub-problems by introducing an auxiliary variable and a quadratic fidelity constraint. Extensive experimental results demonstrate that our method is competitive to the popular methods, including sparsity prior based methods and deep learning based methods, even better than them in the cases of low measurement rates.