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The existing reconstruction algorithms for 2-D signals, most of which convert the original signals into 1-D signals, could be more efficient and accurate. Based on the 2-Dimensional measurement model (2-DMM), a novel recovery algorithm is proposed and then its effectiveness is proved. In 2-DMM, the rows and columns of 2-D signals are measured simultaneously by two independent sensing matrixes. The new algorithm reconstructs the signals as a whole. It relieves the artificial effects and scale expansion caused by the traditional algorithms. Both theoretical analysis and experiment simulation demonstrate that the recovery probability and Reconstruction-SNR performance of the new algorithm are better than those of the existing reconfiguration algorithms under the condition of 2-D measurement. While the operation complexity of the new algorithm is lower than the counterpart of 1-D conversion algorithms. [ABSTRACT FROM AUTHOR]