Abstract: The two-dimensional (2D) sparse signals can be reconstructed by solving a sparse representation problem for multiple measurement vectors (MMVs). However, the extension of the sparse recovery algorithms to the MMV cases may be inefficient if the vectors do not have the same sparsity profile. A sequential down-sampling recovery (SDR) algorithm is proposed to reconstruct the 2D sparse matrix. This method can reduce the sparsity of the signal by constructing down-sampling matrices, and then reconstruct the sparse matrix by sequential observations and reconstructions. Theoretical analysis indicates that the sparse matrix with high sparsity level can be reconstructed with high probability. Experimental results verify the effectiveness of the proposed method in 2D sparse signal and image reconstruction.