In this paper, we propose a novel sparse signal recovery algorithm called the trainable iterative soft thresholding algorithm (TISTA). The proposed algorithm consists of two estimationunits: a linear estimation unit and a minimum mean squared error (MMSE) estimator based shrinkage unit. The error variancerequired in the MMSE shrinkage unit is precisely estimated froma tentative estimate of the original signal. The remarkable featureof the proposed scheme is that TISTA includes adjustable variables that control step size and the error variance for the MMSEshrinkage function. The variables are adjusted by standard deeplearning techniques. The number of trainable variables of TISTA isnearly equal to the number of iteration rounds and is much smallerthan that of known learnable sparse signal recovery algorithms.This feature leads to highly stable and fast training processes ofTISTA. Computer experiments show that TISTA is applicable tovarious classes of sensing matrices, such as Gaussian matrices, binary matrices, and matrices with large condition numbers. Numerical results also demonstrate that, in many cases, TISTA providessignificantly faster convergence than approximate message passing(AMP) and the learned iterative shrinkage thresholding algorithmand also outperforms orthogonal AMP in the NMSE performance.
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