# Why do we regularise in every iteration for imaging inverse problems?

arXiv: https://arxiv.org/abs/2411.00688 · HTML: https://mlsanity.com/paper/2411.00688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates](https://mlsanity.com/paper/2207.12891/) (2022)
- [Higher-order total variation approaches and generalisations](https://mlsanity.com/paper/1912.01587/) (2019)
- [Core Imaging Library -- Part I: a versatile Python framework for tomographic imaging](https://mlsanity.com/paper/2102.04560/) (2021)
- [Core Imaging Library -- Part II: Multichannel reconstruction for dynamic and spectral tomography](https://mlsanity.com/paper/2102.06126/) (2021)
- [Inexact First-Order Primal-Dual Algorithms](https://mlsanity.com/paper/1803.10576/) (2018)
- [Improving "Fast Iterative Shrinkage-Thresholding Algorithm": Faster, Smarter and Greedier](https://mlsanity.com/paper/1811.01430/) (2018)
- [PyHST2: an hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities](https://mlsanity.com/paper/1306.1392/) (2013)
- [Parameter-Free FISTA by Adaptive Restart and Backtracking](https://mlsanity.com/paper/2307.14323/) (2023)

## Abstract (arXiv)

Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational overhead since such evaluation can be costly. In this context, the ProxSkip algorithm, recently proposed for federated learning purposes, emerges as an solution. It randomly skips regularisation steps, reducing the computational time of an iterative algorithm without affecting its convergence. Here we explore for the first time the efficacy of ProxSkip to a variety of imaging inverse problems and we also propose a novel PDHGSkip version. Extensive numerical results highlight the potential of these methods to accelerate computations while maintaining high-quality reconstructions.