Image decomposition based on nonlinear reaction–diffusion systems

Abstract

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneering works suggested such a separation be based on variational formulation and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts. The new model is based on a class of degenerate and singular reaction–diffusion systems coupled by the minimizing total variation flow and the p-Laplace flow. The existence and uniqueness of entropy solutions to the system with BV initial data and Neumann boundary conditions are established by the regularization method. Experimental results illustrate that the new model can preserve textures better than other methods.

Keywords:

• Image decomposition
• degenerate
• singular
• reaction–diffusion systems
• entropy solutions

2010 Mathematics Subject Classifications:

• 94A08
• 35K57

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11971131, U1637208, 61873071, 51476047, 11871133], the Natural Sciences Foundation of Heilongjiang Province [grant number LH2020A004] and the Guangdong Basic and Applied Basic Research Foundation [grant number 2020B1515310010].