Trainable ISTA for Sparse Signal Recovery

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.

10 pages

References in corpus (1)

• Coordinate descent algorithms for lasso penalized regression

Cited by in corpus (38)

• Model-Driven Deep Learning for MIMO Detection
• Learning to Optimize: A Primer and A Benchmark
• Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms
• VPNet: Variable Projection Networks
• Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM
• Solving Sparse Linear Inverse Problems in Communication Systems: A Deep Learning Approach With Adaptive Depth
• Deep Learning-Based Average Consensus
• Chebyshev Inertial Iteration for Accelerating Fixed-Point Iterations
• ADMM-DAD net: a deep unfolding network for analysis compressed sensing
• Deep unfolding of the weighted MMSE beamforming algorithm
• Theoretical Interpretation of Learned Step Size in Deep-Unfolded Gradient Descent
• Deep Learning-Aided Trainable Projected Gradient Decoding for LDPC Codes
• Hubbard-Stratonovich Detector for Simple Trainable MIMO Signal Detection
• Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-driven Tuning Approach
• Deep Learning-Aided Projected Gradient Detector for Massive Overloaded MIMO Channels
• Artificial Intelligence-aided Receiver for A CP-Free OFDM System: Design, Simulation, and Experimental Test
• Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding
• A Model-Driven Deep Learning Network for MIMO Detection
• Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective
• Feasibility-based Fixed Point Networks
• Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork
• Algorithm Unrolling for Massive Access via Deep Neural Network with Theoretical Guarantee
• Trainable Projected Gradient Detector for Sparsely Spread Code Division Multiple Access
• Transfer Learning for Deep-Unfolded Combinatorial Optimization Solver with Quantum Annealer
• Learned Interpretable Residual Extragradient ISTA for Sparse Coding
• Deep Unfolded Multicast Beamforming
• Learning Cluster Structured Sparsity by Reweighting
• Algorithm Unfolding for Block-sparse and MMV Problems with Reduced Training Overhead
• QISTA-Net: DNN Architecture to Solve ${\ell }_q$-norm Minimization Problem and Image Compressed Sensing
• Meta Learning-based MIMO Detectors: Design, Simulation, and Experimental Test
• Proximal Decoding for LDPC-coded Massive MIMO Channels
• Deep Unfolding-Aided Parameter Tuning for Plug-and-Play-Based Video Snapshot Compressive Imaging
• Robust Symbol Detection in Overloaded NOMA Systems
• Model-Driven Deep Learning for Massive Multiuser MIMO Constant Envelope Precoding
• Model-Driven Deep Learning for Massive MU-MIMO with Finite-Alphabet Precoding
• RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems
• Deep unfolding-based output feedback control design for linear systems with input saturation
• Unfolded Deep Neural Network (UDNN) for High Mobility Channel Estimation