# Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements -- the multivariate case

## TL;DR

This paper introduces an iterative method for minimizing the multivariate Potts functional to recover signals with discontinuities from noisy, indirect measurements, with proven convergence and supporting numerical experiments.

## Contribution

A novel iterative minimization strategy for the multivariate Potts functional addressing indirect, noisy data, with theoretical convergence analysis.

## Key findings

- Convergence of the proposed method is established.
- Numerical experiments demonstrate effectiveness in signal recovery.
- Method outperforms existing approaches in handling noise and indirect measurements.

## Abstract

Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics, and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford-Shah functional -- whose discretized version is known as Potts functional -- are advantageous in this scenario, in particular, in connection with segmentation. However, due to their non-convexity, minimization of such functionals is challenging. In this paper we propose a new iterative minimization strategy for the multivariate Potts functional dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.