In this paper we present a new algorithm based on Smoothed ℓ
(SL0), called Block SL0 (BSL0), for Under-determined Systems of Linear Equations (USLE) in which the nonzero elements of the unknown vector occur in clusters. Contrary to the previous algorithms such as Block Orthogonal Matching Pursuit (BOMP) and mixed ℓ
norm, our approach provides a fast algorithm, while providing the same (or better) accuracy. Moreover, we will see experimentally that BSL0 has better performance than SL0, BOMP and mixed ℓ
norm when the number of nonzero elements of the source vector approaches the upper bound of uniqueness theorem.