An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem

Oumaima Benchettou (), Abdeslem Hafid Bentbib () and Abderrahman Bouhamidi ()
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Oumaima Benchettou: University Cadi Ayyad
Abdeslem Hafid Bentbib: University Cadi Ayyad
Abderrahman Bouhamidi: University Littoral, Côte d’Opale

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 1, No 4, 134 pages

Abstract: Abstract We consider the constrained tensorial total variation minimization problem for regularizing ill-posed multidimensional problems arising in many fields, such as image and video processing and multidimensional data completion. The nonlinearity and the non-differentiability of the total variation minimization problem make the resolution directly more complex. The aim of the present paper is to bring together the resolution of this problem using an iterative tensorial double proximal gradient algorithm and the acceleration of the convergence rate by updating some efficient extrapolation techniques in the tensor form. The general structure of the proposed method expands its fields of application. We will restrict our numerical application to the multidimensional data completion which illustrates the effectiveness of the proposed algorithm.

Keywords: Tensorial total variation regularization; Proximal gradient method; Polynomial extrapolation; T-product; Video completion and inpainting (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02234-z

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