Abstract
In the usual non-local variational models, such as the non-local total variations, the image is regularized by minimizing an energy term that penalizes gray-levels discrepancy between some specified pairs of pixels; a weight value is computed between these two pixels to penalize their dissimilarity. In this paper, we impose some regularity to those weight values. More precisely, we minimize a function involving a regularization term, analogous to an H1 term, on weights. Doing so, the finite differences defining the image regularity depend on their environment. When the weights are difficult to define, they can be restored by the proposed stable regularization scheme. We provide all the details necessary for the implementation of a PALM algorithm with proved convergence. We illustrate the ability of the model to restore relevant unknown edges from the neighboring edges on an image inpainting problem. We also argue on inpainting, zooming and denoising problems that the model better recovers thin structures.
Original language | English |
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Pages (from-to) | 296-317 |
Number of pages | 22 |
Journal | Journal of Mathematical Imaging and Vision |
Volume | 59 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Oct 2017 |
Scopus Subject Areas
- Statistics and Probability
- Modelling and Simulation
- Condensed Matter Physics
- Computer Vision and Pattern Recognition
- Geometry and Topology
- Applied Mathematics
User-Defined Keywords
- Image restoration
- Non-convex minimization
- Non-local regularization
- Proximal alternating linearized minimization
- Total variation