A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ ...A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.展开更多
By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-H...By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.展开更多
文摘A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.
基金Project(10171031) supported by the National Natural Science Foundation of China
文摘By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.
