Signal processing techniques for inverse problems in stochastic propagation and scattering channels

Abstract

The basic signal processing techniques associated with inverse problems are signal extraction, deconvolution, signal and signal parameter estimation, channel modeling and characterization. Maximum entropy, minimum cross-entropy, Kullback-Liebler divergence and other information theoretic criteria have been widely used for regularization of underdetermined inversion. We show how maximum entropy and continuous wavelet transforms can be used for spreading function (reflection density function) estimation. If the signal source or receivers are in motion through heterogeneous medium with randomly rough boundaries, propagation and scattering channels are stochastic. Stochastic channels can be characterized by stochastic Greens functions and spreading functions. If the medium probing signals are narrow band, spreading functions are random functions that show how the received signal is spread in delay and Doppler. For wideband probing signals, spreading function spread the received echo in time and time-scale dilation. If the probing signal satisfies admissibility conditions for CWT, wideband spreading functions can be estimated by inverting CWT. Rebollo-Neira and Fernandez-Rubio have shown that the continuous wavelet transform is an optimal solution of the inverse problem, estimation of the spreading function, in a maximum entropy sense. [Work supported by Office of Naval Research Code 333 and Code 321 US.]