Sparsity adaptive matching pursuit (SAMP) is a greedy reconstruction algorithm for compressive sens-ing signals. SAMP reconstructs signals without prior information of sparsity and presents better reconstruction performance for noisy signals compared to other greedy algorithms. However, SAMP still suffers from relatively poor reconstruction quality especially at high compression ratios. In the proposed research, the Wilkinson matrix is used as a sensing matrix to improve the reconstruction quality and to increase the compression ratio of the SAMP technique. Furthermore, the idea of block compressive sensing (BCS) is combined with the SAMP technique to improve the performance of the SAMP technique. Numerous simulations have been conducted to evaluate the proposed BCS-SAMP technique and to compare its results with those of several compressed sensing techniques. Simulation results show that the proposed BCS-SAMP technique improves the reconstruction quality by up to six decibels (dB) relative to the conventional SAMP technique. In addition, the reconstruction quality of the proposed BCS-SAMP is highly comparable to that of iterative techniques. Moreover, the computation time of the proposed BCS-SAMP is less than that of the iterative techniques, especially at lower measurement fractions.