Primal-dual Interior-Point Optimization Based on Majorization-Minimization for Edge-Preserving Spectral Unmixing

Abstract : Primal-dual interior-point methods are used in image processing to solve inversion problems that can be reduced to constrained convex minimization. Such iterative methods require the solution of a sequence of positive definite symmetric linear systems which are used to derive descent directions. This approach is very consuming in terms of computing time and memory usage for large-scale problems, unless the normal matrices have a specific structure. This is the case in the spectral unmixing problem where the normal matrices are block-diagonal when no spatial regularization is considered. Here, we consider the spatially regularized case and we propose to tackle the linear system solving using a majorization-minimization (MM) approach based on separable quadratic majorant functions. The resulting systems have the same structure as in the non-regularized case and can thereby be solved efficiently. The interior-point algorithm is speeded-up while remaining convergent. An example of spectral unmixing is proposed to illustrate the efficiency of this approach
Type de document :
Communication dans un congrès
IEEE International Conference on Image Processing, Oct 2014, Paris, France. 2014
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https://hal.archives-ouvertes.fr/hal-01097605
Contributeur : Saïd Moussaoui <>
Soumis le : samedi 20 décembre 2014 - 05:06:52
Dernière modification le : vendredi 13 octobre 2017 - 14:36:03

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  • HAL Id : hal-01097605, version 1

Citation

Maxime Legendre, Said Moussaoui, Emilie Chouzenoux, Jérôme Idier. Primal-dual Interior-Point Optimization Based on Majorization-Minimization for Edge-Preserving Spectral Unmixing. IEEE International Conference on Image Processing, Oct 2014, Paris, France. 2014. 〈hal-01097605〉

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