Research On Reconstruction Algorithm Of Compressed Sensing

With the extension of intelligent wireless sensor network and the countless sensor products coming into service in 21 th century, great difficulties has been brought to the rapid development of information processing. The information collected by the sensor equipment is unprecedented. Nowadays, most of the sensors collected information with the guidance of The Nyquist sampling theorem, while the information collection technology of The Nyquist sampling theorem imposed restrictions on the sampling rate of minimum information, this technology is the sufficient condition bu not the necessary condition for the reconstruction of original data signal. In recent years, the proposal of compress sensor technology pushed the limitation of minimum information sample rate triggered by Nyquist sampling information collection technology and compress sensor technology got the observed signal on the basis of low information sample rate of signal sparseness, and the technology also reconstruct the observed signal into original signal according to the existing reconstructing algorithm. The thesis reconstruct algorithm function according to the optimized compression perception, and put forward roundabout matching pursuit algorithm and matching pursuit algorithm of predicting support set tortuous on the basis of compressing sensing theory. The major researches contents of the thesis are as follows:Putting forward a roundabout matching pursuit algorithm. Detouring matching pursuit(DMP) is a greedy algorithm of reconstructive sparse signals with low computational complexity, high accuracy and low column-correlation demand for sensing matrix. The increasing and deceasing formulas of the submatrix’s inner-product and the coefficient matrix in the DMP are put forward and proved. By using the inverse of submatrix’s inner-product and the coefficient matrix, DMP could reduce the amount of calculation of residual error’s variable quantity and obtain light computation complexity in the end. In addition, by using the method of decreasing firstly, and then increasing the element of the assumed support set one by one optimally, DMP could improve the reconstructive accuracy and broaden the range of sparsity of reconstructing the sparse signal. The analysis of algorithmic complexity shows that the algorithmic complexity of getting, deceasing and increasing the assumed support set is 2O(K N),O(b(K ?b)N) and O(b(K ?b)N), respectively. The experiment of indirect reconstructive weighted 0-1 sparse signal shows the reconstructive accuracy of the DMP, greedy pursuit algorithm(GPA), subspace pursuit(SP), compressive sampling matching pursuit(CoSaMP) and orthogonal matching pursuit(OMP) are 99%, 65%, 0%, 0% and 13% separately for 0-1 sparse signal with M/ 2 sparsity. The experiment of sparse signals in which the non-zero values obey normal distribution also show the reconstruction accuracy of DMP has obvious superiority.Putting forward the matching pursuit algorithm of predicting support set tortuous. Some compressing perception in the reconstruction algorithm may erase the element in correct supporting set. In order to correct shortcomings, the thesis proposed an improved reconstruction algorithm which could predict the protection of elements in the correcting supporting set. The algorithm updated the unprotected supporting set elements according to minimum residual inner product. Then, in accordance with the projection which the observed vector quantity projected on the corresponding observed submatrix in the unprotected supporting set. Finally, the protected supporting set was output and the original signal was reconstructed. The experiment showed that as for the nonzero value sparseness signal which was normally distributed. The algorithm in this thesis reconstructed the sparseness signal the sparseness of which less than a half of the observed value, and the accuracy rate of it is 86%; as for the noise-including sparseness signal, the reconstruction of it could maintain above 99%, what’s more, it had low volatility.