Matching Pursuit Algorithm For Signal Reconstruction Based On Compressive Sensing

Compressive sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. In this case, the small amount of signal values can be reconstructed accurately when the signal is sparse or compressible. The theory breaks through the traditional Nyquist sampling theory, which is a revolutionary way to achieve the data.In this way, we can overcome an amount of problems such as a great number of sampling data, data physical resources wasting and so on. In this paper, properties of the existing reconstruction algorithms are firstly analyzed. Based on that, the main contributions of this paper are summarized as follows.This paper has reviewed the existing reconstruction algorithms such as OMP, ROMP, CoSaMP, SAMP and done a large number of experiments on them. With a great understanding about the PSNR, relative error, matching ratio and running time of these algorithms, I have find different point of views about optimization algorithms on one-dimensional sparse signal and two-dimensional compressible signals respectively.This paper has analyzed the idea of back researching process in SP and CoSaMP algorithms, which select a number of atoms in each iteration.Nevertheless, we have to remove part of the atoms that we have selected previous because the final support size for reconstruction is determined. So there is a issue that weather the accuracy of the algorithms can be ensured when a part of atoms are removed. In the paper, I have analyzed relationship between this way of selecting atoms and the accuracy of algorithm.The Conclusion shows though we have removed some of the selected atoms from support set, we can still reconstruct the signal accurately with the rest atoms.At last, a new Regularized Adaptive Matching Pursuit (RAMP) algorithm is presented with the idea of regularization. The proposed algorithm could control the accuracy of reconstruction by both the adaptive process which chooses the candidate set automatically and the regularization process which gets the atoms in the final support set although the sparsity of the original signal is unknown. The experimental results show that the proposed algorithm can get better reconstruction performances and it is superior to other algorithms both visually and objectively.