  In this paper, we introduce a weighted $\ell_2/\ell_1$ minimization to
recover block sparse signals with arbitrary prior support information. When
partial prior support information is available, a sufficient condition based on
the high order block RIP is derived to guarantee stable and robust recovery of
block sparse signals via the weighted $\ell_2/\ell_1$ minimization. We then
show if the accuracy of arbitrary prior block support estimate is at least
$50\%$, the sufficient recovery condition by the weighted $\ell_2/\ell_{1}$
minimization is weaker than that by the $\ell_2/\ell_{1}$ minimization, and the
weighted $\ell_2/\ell_{1}$ minimization provides better upper bounds on the
recovery error in terms of the measurement noise and the compressibility of the
signal. Moreover, we illustrate the advantages of the weighted $\ell_2/\ell_1$
minimization approach in the recovery performance of block sparse signals under
uniform and non-uniform prior information by extensive numerical experiments.
The significance of the results lies in the facts that making explicit use of
block sparsity and partial support information of block sparse signals can
achieve better recovery performance than handling the signals as being in the
conventional sense, thereby ignoring the additional structure and prior support
information in the problem.
