Iterative Cosparse Projection Algorithms for the Recovery of Cosparse Vectors
Résumé
Recently, a cosparse analysis model was introduced as an alternative to the standard sparse synthesis model. This model was shown to yield uniqueness guarantees in the context of linear inverse problems, and a new reconstruction algorithm was provided, showing improved performance compared to analysis $\ell_1$ optimization. In this work we pursue the parallel between the two models and propose a new family of algorithms mimicking the family of Iterative Hard Thresholding algorithms, but for the cosparse analysis model. We provide performance guarantees for algorithms from this family under a Restricted Isometry Property adapted to the context of analysis models, and we demonstrate the performance of the algorithms on simulations.
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