A Source Signal Recovery Method for Underdetermined Blind Source Separation based on Shortest Path

A new shortest path source recovery algorithm is presented for source signal recovery issue in underdetermined blind source separation, by which the source signals can be recovered in case the observed signals are no less than two dimensions. In this algorithm, two adjacent observed signals are taken everytime among m observed signals, marked as the ith and jth signals, and form a two-dimensional observed signal combination, i = 1,2,...,m-1, j = i +1. The first and mth signals are used to form another two-dimensional observed signal combination, then m two-dimensional observed signal combinations are obtained. The number of source signals is n, the n signals can be obtained respectively after signal recovery by using each two-dimensional observed signal combination A matrix (i.e., (s) over tilde (p,q,:) = [(s) over cap (1,1,:),(s) over cap (1,2,:),...,(s) over cap (1, n,:),(s) over cap (2,1,:),...,(s) over cap (m,n,:)](T)) which is a mn-dimensional vector combination matrix can be obtained using each signal combination A mnxmn-dimensional square matrix can be gotten by calculating the vector angle between rows of (s) over tilde (p,q,:) matrix, for the first n rowsxmn columns, position the vector where the matrix elements are between 0 and theta(0). The mean is calculated for the signal vector with angle smaller than theta(0) as the estimate of the source signals. Thus, the estimates (s) over cap (1,:), (s) over cap (2,:),...,(s) over cap (n,:) of n source signals can be obtained eventually. The method presented provides a new option for solving underdetermined blind source signal recovery problem.