Committee:

Dr. Justin Romberg, ECE, Chair , Advisor

Dr. Karim Sabra, ME

Dr. Mark Davenport, ECE

Dr. James McClellan, ECE

Dr. Christopher Rozell, ECE

Abstract:

The objective of this thesis is to develop new techniques for solving the multichannel blind deconvolution problem and to implement these techniques in an acoustic waveguide environment.  We revisit this classical problem by investigating channel models and recovery methods.  We show how to use a priori information about channels to build appropriate channel models that, in turn, can be incorporated into our methods.  Both linear and bilinear channel models will be investigated in our study.  Our first method views solving the multichannel deconvolution problem as solving a system of bilinear equations, which in turn can be recast as recovering a low-rank matrix from a set of linear observations.  Our second method furthers our knowledge in the classical subspace method for blind deconvolution, and efficient and guaranteed algorithms are presented.  We also extend our method to a multiple-source multiple-channel convolution scenario and develop a source separation framework.  Moreover, we investigate a subspace learning method for multichannel deconvolution by using multiple snapshots of measurements.