# A nonstandard higher-order variational model to speckle noise removal and thin-structure detection

## TL;DR

This paper introduces a multiscale, higher-order PDE-based variational model utilizing $p(
abla)$-Kirchhoff energy for effective speckle noise removal and thin-structure detection, combining topological gradient and split Bregman methods.

## Contribution

It develops a novel adaptive nonlinear PDE model with variable exponents for image denoising and feature preservation, integrating topological gradient detection and advanced numerical techniques.

## Key findings

- Outperforms classical variational models like TVL and biharmonic in noise removal.
- Effectively detects thin structures while reducing speckle noise.
- Numerical results demonstrate improved feature preservation and noise suppression.

## Abstract

In this work, we propose a multiscale approach for a nonstandard higher-order PDE based on the $p(\cdot)$-Kirchhoff energy. First, we consider a topological gradient approach for a semilinear case in order to detect important object of image. Then, we consider a fully nonlinear $p(\cdot)$-Kirchhoff equation with variables exponent functions that are chosen adaptively based on the map furnished by the topological gradient in order to preserve important features of the image. Then, we consider the split Bregman method for the numerical implementation of our proposed model. We compare our model with other classical variational approaches such that the TVL and biharmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.

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Source: https://tomesphere.com/paper/1706.06190