# Complex Trainable ISTA for Linear and Nonlinear Inverse Problems

arXiv: https://arxiv.org/abs/1904.07409 · HTML: https://mlsanity.com/paper/1904.07409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Algorithm Unrolling for Massive Access via Deep Neural Network with Theoretical Guarantee](https://mlsanity.com/paper/2106.10426/) (2021)

## Abstract (arXiv)

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.