Constrained tensorial total variation problem based on an alternating conditional gradient algorithm
The present paper aims to regularize ill-posed high-dimensional problems using a constrained total variation minimization approach. The analysis of the continuous model via the dual formulation converts this minimization problem into a constrained minimax problem. Three main issues stand before the...
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| Published in: | Journal of computational and applied mathematics Vol. 451; p. 116018 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.12.2024
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| Subjects: | |
| ISSN: | 0377-0427 |
| Online Access: | Get full text |
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| Summary: | The present paper aims to regularize ill-posed high-dimensional problems using a constrained total variation minimization approach. The analysis of the continuous model via the dual formulation converts this minimization problem into a constrained minimax problem. Three main issues stand before the resolution of this problem: The minimization over a constraint, the high dimensional representation of the model, and the non-linearity and non-differentiability of the cost function. On the one hand, multidimensional data analysis will be performed using the tensor representation. On the other hand, a new alternating approach based on a proposed pseudo-Lagrangian operator will be developed to deal with the non-linearity and the non-differentiability of this constrained optimization problem. The proposed technique aims to decompose the main tensorial problem into feasible subproblems that can be solved using the conditional gradient method. The convergence of the proposed algorithm is proved and some numerical results are given to illustrate the effectiveness of the presented approach in different fields of image and video processing. |
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| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2024.116018 |