Blind system identification using normalized Fourier coefficient gradient vectors obtained from time-frequency entropy-based blind clustering of datawavelets

A method for the blind identification of spatially varying transfer functio ns found in various remote sensing applications such as medical imagery, ra dar, sonar, and seismology is described. The techniques proposed herein are based on model matching of Fourier coefficient sensitivity vectors of a kn own transfer function, which can be nonlinear in the parameters, with a set of eigenvectors obtained from data covariance matrices. One distinction be tween this technique and usual channel subspace methods is that no FIR stru cture for the individual transfer functions is assumed. Instead we assume t hat the frequency response as a function of the parameters is known as is o ften the case in wave transmission problems. A channel identification proce dure based on subspace matching is proposed. The procedure matches the eige nvectors of the signal deviation covariance matrix to a set of scaled and e nergy-normalized sensitivity vectors. For the case where neither the number of channels, the model parameters of each channel nor the membership assig nment of data traces to the channels is known, we propose a novel prelimina ry clustering process. By separating the data into clusters of modest varia bility such that the measurements are linear with the parameters, we are ab le to deduce all of the above. The clustering is based on feature vectors o btained from a time-frequency entropy measure, also a novelty of our paper. To support the theory developed, we include parameter estimation results b ased on simulated data backscattered from a synthetic multi-layer structure , (C) 1999 Academic Press.