A new cartoon plus texture image decomposition model based on the Sobolev space

Image decomposition aims to decompose a given image into one structural component and another oscillatory component. In most variational decomposition models, the structural component is often measured by the total variation norm and the oscillatory component is measured by its dual norm or others. In this paper, we let the structural component belong to the bounded variation space, the oscillatory texture be in the Sobolev space W--1,W- 1, and the H-1 norm model the residual part. The new model combines the advantages of total variation regularization and weaker norm oscillatory component modeling, and it can well decompose the cartoon and texture while preserving some edges and contours. To solve this optimal problem, an effective numerical algorithm based on the splitting versions of augmented Lagrangian method is discussed in detail. Experimental results are reported to show the visual qualities compared with some state-of-the-art methods.

Automated summary

This paper introduces a method for decomposing an image into structural and oscillatory components. By placing the structural component in the bounded variation space and the oscillatory texture in the Sobolev space, with the residual part modeled by the H-1 norm, the new model effectively decomposes the image while preserving some edges and contours.