Sparsity adaptive matching pursuit(SAMP)is a greedy reconstruction algorithm for compressive sensing signals.SAMP reconstructs signals without prior information of sparsity and presents better reconstruction performan...Sparsity adaptive matching pursuit(SAMP)is a greedy reconstruction algorithm for compressive sensing signals.SAMP reconstructs signals without prior information of sparsity and presents better reconstruction performance for noisy signals compared to other greedy algorithms.However,SAMP still suffers from relatively poor reconstruction quality especially at high compression ratios.In the proposed research,the Wilkinson matrix is used as a sensing matrix to improve the reconstruction quality and to increase the compression ratio of the SAMP technique.Furthermore,the idea of block compressive sensing(BCS)is combined with the SAMP technique to improve the performance of the SAMP technique.Numerous simulations have been conducted to evaluate the proposed BCS-SAMP technique and to compare its results with those of several compressed sensing techniques.Simulation results show that the proposed BCS-SAMP technique improves the reconstruction quality by up to six decibels(d B)relative to the conventional SAMP technique.In addition,the reconstruction quality of the proposed BCS-SAMP is highly comparable to that of iterative techniques.Moreover,the computation time of the proposed BCS-SAMP is less than that of the iterative techniques,especially at lower measurement fractions.展开更多
Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leadi...Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.展开更多
文摘Sparsity adaptive matching pursuit(SAMP)is a greedy reconstruction algorithm for compressive sensing signals.SAMP reconstructs signals without prior information of sparsity and presents better reconstruction performance for noisy signals compared to other greedy algorithms.However,SAMP still suffers from relatively poor reconstruction quality especially at high compression ratios.In the proposed research,the Wilkinson matrix is used as a sensing matrix to improve the reconstruction quality and to increase the compression ratio of the SAMP technique.Furthermore,the idea of block compressive sensing(BCS)is combined with the SAMP technique to improve the performance of the SAMP technique.Numerous simulations have been conducted to evaluate the proposed BCS-SAMP technique and to compare its results with those of several compressed sensing techniques.Simulation results show that the proposed BCS-SAMP technique improves the reconstruction quality by up to six decibels(d B)relative to the conventional SAMP technique.In addition,the reconstruction quality of the proposed BCS-SAMP is highly comparable to that of iterative techniques.Moreover,the computation time of the proposed BCS-SAMP is less than that of the iterative techniques,especially at lower measurement fractions.
基金The Fundamental Research Funds for the Central Universities, China (No.10D10908)
文摘Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.
