Quantum correlated imaging technology adopts single-point intensity detecting, huge information storage, slow imaging speed, so faster image reconstruction algorithm was required. The simulation of samples with image reconstructing algorithm was based on statistical arithmetic and compressed sensing respectively. The inputs of the compressed sensing algorithm are sparse images which are calculated with discrete cosine transform (DCT) and Gauss random matrices, reconstructing image with orthogonal matching pursuit (OMP). The result shows that the correlated imaging algorithm based on compressed sensing can lessen the number of measurements and save data space and speed. Therefore, the study of quantum correlated imaging image reconstruction algorithm has great significance for lessening the number of samples and improving imaging speed.