A new cartoon + 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....

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Bibliographic Details
Published in:Signal, image and video processing image and video processing, 2022, Vol.16 (6), p.1569-1576
Main Authors: Xu, Jianlou, Shang, Wanqing, Hao, Yan
Format: Article
Language:English
Subjects:
Algorithms
Computer Imaging
Computer Science
Decomposition
Image Processing and Computer Vision
Multimedia Information Systems
Numerical analysis
Original Paper
Pattern Recognition and Graphics
Regularization
Signal,Image and Speech Processing
Sobolev space
Texture
Vision
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Summary: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 , 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.
ISSN:1863-1703
1863-1711
DOI:10.1007/s11760-021-02111-0