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

International audienceRecently, 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