# On Convergent Finite Difference Schemes for Variational - PDE Based Image Processing

Source: [On Convergent Finite Difference Schemes for Variational - PDE Based Image Processing](<https://www.sota2.com/research/paper/68fa545b1e209131ce98ae93>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-05T05:00:20.018Z

Authors: V. B. S. Prasath, Juan C. Moreno

Published: 2013-09-16T23:07:39.000Z

## Abstract

We study an adaptive anisotropic Huber functional based image restoration scheme. By using a combination of L2-L1 regularization functions, an adaptive Huber functional based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrate that the best convergence rates are obtained for our algorithm.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Restoration on Cameraman gray scale image](<https://www.sota2.com/research/sota/image-restoration-on-cameraman-gray-scale-image.md>): Image Restoration; Cameraman gray scale image; PSNR: 25.4.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1310.7443>)

[PDF](<https://arxiv.org/pdf/1310.7443.pdf>)