Exact solutions for the denoising problem of piecewise constant images in dimension one

TL;DR

This paper derives explicit solutions for the total variation denoising problem with an $L^p$ fidelity term ($p>1$) specifically for one-dimensional piecewise constant images, providing a precise analytical approach.

Contribution

It introduces an explicit solution method for the TV denoising problem with $L^p$ fidelity for one-dimensional piecewise constant data, a case not previously solved analytically.

Findings

Explicit solutions are derived for the denoising problem.

The method applies to $L^p$ fidelity with $p>1$.

Provides a new analytical tool for one-dimensional image processing.

Abstract

In this paper we propose a method to determine explicitly the solution of the total variation denoising problem with an $L^p$ fidelity term, where $p>1$, for piecewise constant initial data in dimension one.