# Proximal Gradient Algorithms: Applications in Signal Processing

arXiv: https://arxiv.org/abs/1803.01621 · HTML: https://mlsanity.com/paper/1803.01621/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Discrete Aware Matrix Completion via Convexized ℓ0-Norm Approximation](https://mlsanity.com/paper/2405.02101/) (2024)
- [Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspective](https://mlsanity.com/paper/2603.23831/) (2026)
- [Robust Non-negative Proximal Gradient Algorithm for Inverse Problems](https://mlsanity.com/paper/2510.23362/) (2025)

## Abstract (arXiv)

Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton methods with forward-adjoint oracles to tackle large-scale problems and reduce the computational burden of many applications. These proximal gradient algorithms are here described in an easy-to-understand way, illustrating how they are able to address a wide variety of problems arising in signal processing. A new high-level modeling language is presented which is used to demonstrate the versatility of the presented algorithms in a series of signal processing application examples such as sparse deconvolution, total variation denoising, audio de-clipping and others.