# A forward-backward view of some primal-dual optimization methods in image recovery

arXiv: https://arxiv.org/abs/1406.5439 · HTML: https://mlsanity.com/paper/1406.5439/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2014.

## Built on by (most cited first, 5 of 5)

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- [No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization](https://mlsanity.com/paper/2111.11309/) (2021)
- [Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning](https://mlsanity.com/paper/2109.12222/) (2021)
- [Contractivity and linear convergence in bilinear saddle-point problems: An operator-theoretic approach](https://mlsanity.com/paper/2410.14592/) (2024)

## Abstract (arXiv)

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide efficient solutions to large-scale optimization problems. The objective of this paper is to show that a number of existing algorithms can be derived from a general form of the forward-backward algorithm applied in a suitable product space. Our approach also allows us to develop useful extensions of existing algorithms by introducing a variable metric. An illustration to image restoration is provided.