SURE-TISTA: A Signal Recovery Network for Compressed Sensing

Deep neural network (DNN) has a wide range of applications in various fields, including solving sparse inverse problems. In this paper, we propose a novel network called the Stein's unbiased risk estimate based-trainable iterative thresholding algorithm (SURE-TISTA) for sparse signal recovery problems. Without prior information, SURE-TISTA outperforms TISTA, an algorithm based on the minimum mean squared error (MMSE) estimator. SURE-TISTA also shows a great robustness in many cases including large-scale and large-variance problems. Meanwhile, SURE-TISTA uses fewer learnable variables to achieve similar performance as learned approximate message passing (LAMP), which has more learnable parameters. Without any error measure estimator, SURE-TISTA achieves a near MMSE-based performance. Our numerical results indicate that SURE-TISTA is superior to TISTA and other traditional algorithms in many aspects, which can be promising in image denoising.