In practical applications, some sparse signals have structural characteristics of block sparsity. Under the hypothesis of removing the requirements on the noise in recent literature concerning the \(\ell _2/\ell _p\,(0<p\le 1)\) minimization method, uniform block restricted isometry property (B-RIP) condition is established for the stable recovery of approximately block k-sparse signals with partial block support information by employing the weighted \(\ell _2/\ell _p\) minimization method. Compared with the state-of-the-art results, the newly-obtained results present more relaxed sufficient condition for block sparse signal recovery, and meanwhile provide more precise reconstruction error estimations in different noise settings. Numerical experiments demonstrate that the new method exhibits a substantial increase in the reconstruction quality for highly undersampled block structural signals.
