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We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0<p\leq1)$ minimization for block sparse signal reconstruction from compressedmeasurements when partial block support information is available. We show thatthe block $p$-restricted isometry property (RIP) can ensure the robustrecovery. Moreover, we present the sufficient and necessary condition for therecovery by using weighted block $p$-null space property. The relationshipbetween the block $p$-RIP and the weighted block $p$-null space property hasbeen established. Finally, we illustrate our results with a series of numericalexperiments.

Recovery analysis for weighted mixed $\ell_2/\ell_p$ minimization with $0