Keeping less valid data to obtain necessary information has become a new requirement in the signal-processing field. The paper employs adaptive dictionary for sparse representation, introduces a characteristic-weighting coefficient to offer detailed image information, and meanwhile performs Schmidt orthogonalization with the combination of Gaussian random measurement matrix to minimize the correlation of vectors in matrix. It raises the figure structural group sparse representation (FSGSR) algorithm based on matrix orthogonalization. Experiments indicate that this improved image reconstruction algorithm has enhanced the reconstructed image quality compared with typical algorithms during same time length.