The best of both worlds: synthesis-based acceleration for physics-driven cosparse regularization

Srdan Kitic 1 Nancy Bertin 1 Rémi Gribonval 1
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Recently, a regularization framework for ill-posed inverse problems governed by linear partial differential equations has been proposed. Despite nominal equivalence between sparse synthesis and sparse analysis regularization in this context , it was argued that the latter is preferable from computational point of view (especially for huge scale optimization problems arising in physics-driven settings). However, the synthesis-based optimization benefits from simple, but effective all-zero initialization, which is not straightforwardly applicable in the analysis case. In this work we propose a multiscale strategy that aims at exploiting computational advantages of both regularization approaches.
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Srdan Kitic, Nancy Bertin, Rémi Gribonval. The best of both worlds: synthesis-based acceleration for physics-driven cosparse regularization. iTwist 2016 - International Traveling Workshop on Interactions Between Sparse Models and Technology, Aug 2016, Aalborg, Denmark. 2016. 〈hal-01329051〉

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