Trainable ISTA for Sparse Signal Recovery

TLDR

The paper proposes Trainable ISTA (TISTA), a novel sparse signal recovery algorithm. TISTA alternates a linear estimation unit with an MMSE‑based shrinkage unit, estimating the error variance from a tentative signal and learning step‑size and variance parameters through standard deep‑learning techniques, resulting in far fewer trainable variables than existing learnable algorithms. Experiments show that TISTA trains stably and quickly, works with Gaussian, binary, and ill‑conditioned matrices, and converges significantly faster than AMP and LISTA.

Abstract

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.