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1 TU Darmstadt - Technische Universität Darmstadt 2 EE-Technion - Department of Electrical Engineering - Technion 3 Thoth - Apprentissage de modèles à partir de données massives Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann

Abstract : We propose a new algorithm to learn a dictionary along with sparse representations from signal measurements without phase. Specifically, we consider the task of reconstructing a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider sparse phase retrieval when the sparsifying dictionary is not known in advance, and we learn a dictionary such that each patch of the reconstructed image can be sparsely represented. Our numerical experiments demonstrate that our proposed scheme can obtain significantly better reconstructions for noisy phase retrieval problems than methods that cannot exploit such - hidden - sparsity.

Author: Andreas Tillmann - Yonina Eldar - Julien Mairal -

Source: https://hal.archives-ouvertes.fr/


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