# Learning optimal nonlinearities for iterative thresholding algorithms

arXiv: https://arxiv.org/abs/1512.04754 · HTML: https://mlsanity.com/paper/1512.04754/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2015.

## Built on by (most cited first, 4 of 4)

- [SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees](https://mlsanity.com/paper/2101.09379/) (2021)
- [Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks](https://mlsanity.com/paper/2112.04364/) (2021)
- [Learning Generative Prior with Latent Space Sparsity Constraints](https://mlsanity.com/paper/2105.11956/) (2021)
- [A statistical perspective on algorithm unrolling models for inverse problems](https://mlsanity.com/paper/2311.06395/) (2023)

## Abstract (arXiv)

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.