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In this work, we consider the problem of recovering analysis-sparse signalsfrom under-sampled measurements when some prior information about the supportis available. We incorporate such information in the recovery stage by suitablytuning the weights in a weighted $\ell_1$ analysis optimization problem.Indeed, we try to set the weights such that the method succeeds with minimumnumber of measurements. For this purpose, we exploit the upper-bound on thestatistical dimension of a certain cone to determine the weights. Our numericalsimulations confirm that the introduced method with tuned weights outperformsthe standard $\ell_1$ analysis technique.

Improved Recovery of Analysis Sparse Vectors in Presence of Prior Information