Image denoising by a novel variable-order total fractional variation model. (English) Zbl 1472.94006
Image denoising has two opposite goals: removing unwanted noise from smooth areas but preserving edges and textures. The increasingly popular fractional-order variation methods for image denoising depend on parameter \(\alpha \), \(1 \leqslant \alpha \leqslant 2\). If \(\alpha \) is close to 1, edges (textures) will be recovered well, but in smooth areas may appear piecewise constant regions (the staircase effect); if \(\alpha \) is close to 2, smooth areas will be recovered fine, but there may appear problems with edges. Here, a new two-adaptive denoising scheme for monochrome images is introduced: first the character of an area is recognized by indicator function \(g(v)\) using the derivative of the image and the fractional parameter will be near 1 near edges and near 2 in smooth areas. This leads to minimization of an integral of a lower semicontinuous function in Banach space. The authors show the existence and uniqueness of solution and provide some test examples of denoising monochrome images.
Reviewer: Jaak Henno (Tallinn)
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 26A33 | Fractional derivatives and integrals |
| 62H35 | Image analysis in multivariate analysis |
| 65K05 | Numerical mathematical programming methods |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
| 74G75 | Inverse problems in equilibrium solid mechanics |
Keywords:
image denoising; variable-order fractional calculus; variational methods; split Bergman methodReferences:
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