Performance Analysis of Joint-Sparse Recovery from Multiple Measurements and Prior Information via Convex Optimization

We address the problem of compressed sensing with multiple measurement vectors associated with prior information in order to better reconstruct an original sparse matrix signal. $\ell_{2,1}-\ell_{2,1}$ minimization is used to emphasize co-sparsity property and similarity between matrix signal and prior information. We then derive the necessary and sufficient condition of successfully reconstructing the original signal and establish the lower and upper bounds of required measurements such that the condition holds from the perspective of conic geometry. Our bounds further indicates what prior information is helpful to improve the the performance of CS. Experimental results validates the effectiveness of all our findings.