Method for determining true spectrum from measurement spectrum

摘要

(57) in determining the true spectrum from the measured spectrum using [Abstract] maximum entropy algorithm, to determine the eigenvalues ​​of (10 ⁵ to 10 ⁴ is the order of N) N × N-type matrix of large dimension impractical most, or, it is not practical at all in some cases. In accordance with the present invention, a large matrix of this type is divided into sub-matrices large number of very small it is the main diagonal of the diagonal or larger matrix. The set of eigenvalues ​​to be determined is formed by eigenvalues ​​of the submatrices of all can be determined more quickly. Because of the characteristics of the Toeplitz matrix part, these eigenvalues ​​can be determined very quickly by using the Fourier transform of a single row of the submatrix. Thus by using the set of eigenvalues ​​obtained, the true spectrum is determined by using a minimization algorithm. Convergence speed of the minimization algorithm is significantly improved by adding the variable minimization process of random noise, to reduce to zero the iteration step a number of the random noise values.