In this paper, we propose a novel sparse signal recovery algorithm called
Trainable ISTA (TISTA). The proposed algorithm consists of two estimation units
such as a linear estimation unit and a minimum mean squared error (MMSE)
estimator-based shrinkage unit. The estimated error variance required in the
MMSE shrinkage unit is precisely estimated from a tentative estimate of the
original signal. The remarkable feature of the proposed scheme is that TISTA
includes adjustable variables controlling a step size and the error variance
for the MMSE shrinkage. The variables are adjusted by standard deep learning
techniques. The number of trainable variables of TISTA is equal to the number
of iteration rounds and it is much smaller than that of known learnable sparse
signal recovery algorithms. This feature leads to highly stable and fast
training processes of TISTA. Computer experiments show that TISTA is applicable
to various classes of sensing matrices such as Gaussian matrices, binary
matrices and matrices with large condition numbers. Numerical results also
demonstrate that TISTA shows significantly faster convergence than those of AMP
and LISTA in many cases.

本文提出了一种名为 TISTA 的新型稀疏信号恢复算法，采用了可调整参数控制步长和误差方差的最小均方误差收缩单元，并通过标准深度学习技术调整这些变量，实验表明，TISTA 适用于各种传感矩阵，并且收敛速度明显快于 AMP 和 LISTA。