A Source Signal Recovery Method for Underdetermined Blind Source Separation based on Shortest Path
Keywords:
Shortest Path Method, Source Signal Recovery, Sparsity, Underdetermined Blind Source SeparationAbstract
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 twodimensional observed signal combination, then m twodimensional 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(p,q,:)=[sˆ(1,1,:), sˆ(1,2,:),..., sˆ(1,n,:), sˆ(2,1,:),... , sˆ(m,n,:)T]) which is a mn-dimensional vector combination matrix can be obtained using each signal combination A mnmn-dimensional square matrix can be gotten by calculating the vector angle between rows of s(p,q,:) matrix, for the first n rowsmn columns, position the vector where the matrix elements are between 0 and θ0. The mean is calculated for the signal vector with angle smaller than θ0 as the estimate of the source signals. Thus, the estimates sˆ(1,:), sˆ(2,:),..., sˆ(n,:) of n source signals can be obtained eventually. The method presented provides a new option for solving underdetermined blind source signal recovery problem.
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