In this work, we present a full-reference stereo image quality assessment algorithm that is based on the sparse representations of luminance images and depth maps. The primary challenge lies in dealing with the sparsity of disparity maps in conjunction with the sparsity of luminance images. Although analysing the sparsity of images is sufficient to bring out the quality of luminance images, the effectiveness of sparsity in quantifying depth quality is yet to be fully understood. We present a full reference Sparsity-based Quality Assessment of Stereo Images (SQASI) that is aimed at this understanding. © 2016 IEEE.