Nonlinear Functions in Learned Iterative Shrinkage-Thresholding Algorithm for Sparse Signal Recovery

Compressive sensing requires fewer measurements than Nyquist rate to recover sparse signals, leading to processing and energy saving. The efficiency of this technique strongly depends on the quality of the considered sparse recovery algorithm. This work focuses on a learned iterative shrinkage-thresholding algorithm where iterations are related to layers of a neural network. We analyze the performance of this algorithm for different shrinkage functions. A decrease up to 9dB in the NMSE value is achieved by choosing appropriate shrinkage function. Moreover, the estimation performance can be close to the theoretical performance bound, showing deep learning as a promising tool for sparse signal estimation. This work can be applied in several areas such as image processing, Internet of Things (IoT), cognitive radio networks, and sparse channel estimation for wireless communications.