Multichannel Deconvolution with Applications to Signal and Image Processing

摘要

Problems in harmonic analysis and synthesis are intertwined with theirapplications in signal and image processing. Two direct applications of these theories are in the development of multichanriel deconvolution and parameter estimation. The first is the recovery of information from linear. translation invariant systems. The work in this area has progressed in a variety of areas. The general theory, and its relationship to wavelet and Gabor analysis was developed. A very general method for the creation of strongly coprime deconvolvers was constructed. and the interaction of deconvolution and sampling was developed. Properly sampled signals can be deconvolved and reconstructed as analog signals simultaneously. Sampling theory also provided a new method for constructing deconvolvers. Work was done on deconvolving Wiener filters. Very simply, the main idea of this work is to optimally deconvolve a signal from a noisy environment. The theory was extented by increasing the types of systems that can be modeled, including linear combinations of n-fold convolutions of characteristic functions with equally spaced knots (cardinal splines) and truncated sinc and truncated Gaussian functions. Finally, the theory was simulated, providing the first step in linking the theory to its many potential applications. The second area is in the develpment of computationally straightforward and very general algorithms for several classes of problems in estimation. Particular items investigated included development of computationally stralghtforward techniques for simple spectral analysis of a very broad class of periodic processes and the extention of these techniques to the analysis of data generated by multiple periodic generators, including the deinterleaving of these generators. This work is may be applied to communications systems radar and sonar biomedical systems etc.