Method of determining an intrinsic spectrum from a measured spectrum

摘要

In determining an intrinsic spectrum from a measured spectrum using the Maximum Entropy Algorithm, it is hardly or even not at all practical to determine the eigenvalues of an NxN matrix of large dimensions (N of the order of from 104 to 105). According to the invention such a large matrix is subdivided into a large number of much smaller partial matrices that are located on the diagonal or trace of the large matrix. The set of eigenvalues to be determined then consists of all eigenvalues of the partial matrices which can be determined much faster. Because of the Toeplitz-like character of the partial matrices, their eigenvalues can be determined very fast by Fourier transformation of a single row of such a matrix. Using the set of eigenvalues thus obtained, the intrinsic spectrum is determined by means of a minimizing algorithm. The convergence rate of the minimizing algorithm can be highly enhanced by adding a random noise value to the variables of the minimizing process and by decreasing that noise value to zero in a number of iteration steps.