期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 67, 期 12, 页码 3113-3125出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2019.2912879
关键词
Compressed sensing; machine learning; supervised learning
资金
- Japan Society for the Promotion of Science (JSPS) [16H02878, 19H02138, 17H06758]
- Grants-in-Aid for Scientific Research [17H06758] Funding Source: KAKEN
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 estimation units: a linear estimation unit and a minimum mean squared error (MMSE) estimator based shrinkage unit. The 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 that control step size and the error variance for the MMSE shrinkage function. The variables are adjusted by standard deep learning techniques. The number of trainable variables of TISTAis nearly equal to the number of iteration rounds and 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, in many cases, TISTA provides significantly faster convergence than approximate message passing (AMP) and the learned iterative shrinkage thresholding algorithm and also outperforms orthogonal AMP in the NMSE performance.
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