# Adaptive diffusion constrained total variation scheme with application to `cartoon + texture + edge' image decomposition

arXiv: https://arxiv.org/abs/1505.00866 · HTML: https://mlsanity.com/paper/1505.00866/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2015.

## Built on by (most cited first, 1 of 1)

- [Semi-sparsity Priors for Image Structure Analysis and Extraction](https://mlsanity.com/paper/2308.09141/) (2023)

## Abstract (arXiv)

We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV) scheme for image adaptive decomposition. An adaptive weight along with TV regularization splits a given image into three components representing the geometrical (cartoon), textural (small scale - microtextures), and edges (big scale - macrotextures). We study the wellposedness of the coupled variational-PDE scheme along with an efficient numerical scheme based on Chambolle's dual minimization method. We provide extensive experimental results in cartoon-texture-edges decomposition, and denoising as well compare with other related variational, coupled anisotropic diffusion PDE based methods.