Fast reconstruction method for compressed sensing model with semi-tensor product - Jinming WANG; Shiping YE; Lizhe YU; Sen XU; Yanjun JIANG (Tongxin xuebao)
To reduce the storage space of random measurement matrix and improve the reconstruction efficiency for compressed sensing (CS),a new sampling approach for CS with semi-tensor product (STP-CS) was proposed.The proposed approach generated a low dimensional random measurement matrix to sample the sparse signals.Then the solutions of the sparse vector were estimated group by group with a lq-minimization (0＆lt;q＆lt;1) iteratively re-weighted least-squares (IRLS) algorithm.Compared with traditional compressed sensing methods,the proposed approach outperformed conventional CS in speed of reconstruction and that it also obtained comparable quality in the reconstruction.Numerical experiments were conducted using gray-scale images,the peak signal-to-noise ratio (PSNR) and the reconstruction time of the reconstruction images were compared with the random matrices with different dimensions.Comparisons were also conducted with other low storage techniques.Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to M t <mtext>×</mtext> N t and decrease tow orders of magnitude of time that for conventional CS,while maintaining the reconstruction quality.Numerical results also show that the reconstruction time can be effectively improved 260 for the image size of 1 024×1 024.