Complex Trainable ISTA for Linear and Nonlinear Inverse Problems

TL;DR

This paper introduces C-TISTA, a trainable iterative algorithm for complex-field signal recovery in noisy linear and nonlinear inverse problems, demonstrating superior performance with efficient training.

Contribution

The paper presents C-TISTA, a novel deep unfolding-based algorithm with trainable complex-valued functions for improved complex signal recovery.

Findings

C-TISTA outperforms existing algorithms in signal recovery accuracy.

C-TISTA requires only a small number of trainable parameters.

Efficient training process demonstrated through numerical results.

Abstract

Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.