Iterative Cosparse Projection Algorithms for the Recovery of Cosparse Vectors

Abstract : 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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The 19th European Signal Processing Conference (EUSIPCO‐2011), 2011, Barcelona, Spain. 2011
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Raja Giryes, Sangnam Nam, Rémi Gribonval, Mike E. Davies. Iterative Cosparse Projection Algorithms for the Recovery of Cosparse Vectors. The 19th European Signal Processing Conference (EUSIPCO‐2011), 2011, Barcelona, Spain. 2011. 〈inria-00611592〉

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