Compressed sensing [1], [2] is one of the most exciting topics of present-day signal processing. Signal reconstruction from its low-dimensional representation becomes a possibility, given the sparse nature of the signal and, incoherence and/or restricted isometry property (RIP) [2] of the sensing/measurement process. In this regard, a number of approaches can be used, e.g., basis pursuit (BP) [3], least absolute shrinkage and selection operator (LASSO) [4] and greedy algorithms [5]. In order to exploit the structure of the signal being sensed, a number of variants of LASSO have become popular, e.g., group LASSO (G-LASSO) [6], sparse group LASSO (SG-LASSO) [7] and fused LASSO (F-LASSO) [8], etc. In this letter we propose new LASSO formulations to handle block sparse smooth signals.