A New TV-Stokes Model for Image Deblurring and Denoising with Fast Algorithms

The famous TV-Stokes models, which improve the restored images comfortable, have been very successful in image denoising. In this paper, we propose a new TV-Stokes model for image deblurring with a good geometry explanation. In the tangential field smoothing, the data fidelity term is chosen to meas...

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Bibliographic Details
Published in:Journal of scientific computing 2017-08, Vol.72 (2), p.522-541
Main Authors: Jia, Zhi-Gang, Wei, Musheng
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Data smoothing
Geometry
Image reconstruction
Image restoration
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Noise reduction
Regularization
Robustness (mathematics)
Smoothing
Theoretical
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Summary:The famous TV-Stokes models, which improve the restored images comfortable, have been very successful in image denoising. In this paper, we propose a new TV-Stokes model for image deblurring with a good geometry explanation. In the tangential field smoothing, the data fidelity term is chosen to measure the distance between the solution and the orthogonal projection of the tangential field of the observation image onto the range of the conjugate of the blurry operator, while the total variation of the solution is chosen as the regularization term. In the image reconstruction, we compute the smoothing part of the image from the smoothed tangential field for the first step, and use an anisotropic TV model to obtain the “texture” part of the deblurred image. The solvability properties for the minimization problems in two steps are established, and fast algorithms are presented. Numerical experiments demonstrate that the new deblurring model can capture the details of images hidden in the blurry and noisy image, and the fast algorithms are efficient and robust.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0368-0