Research Interests

Dr. Noonan has thirty-five years experience in the areas of digital signal processing, probabilistic and statistical modeling and statistical communications theory. His primary research activities concern the application of statistical communication theory and digital signal processing to the problems of optimal detection and estimation of signals in noise. Specific application areas include Channel Modeling (Blind Equalization), Spectral Estimation, Image Enhancement, Deconvolution, Time Varying System Modeling, and Radar Signal Processing.

One major area of Dr. Noonan's research concerns the application of concepts from Information Theory to the important problems of deconvolution and system modeling. In this work he has developed a general iterative mapping derived using the mutual information functional from Information Theory to establish a criterion for optimality in solving problems of signal and image restoration and resolution enhancement. Here a mathematical structure is defined and the convergence of the mapping is established both in the general formulation and for particular examples. Some popular techniques for signal restoration, such as that proposed by Van Cittert and derived independently of Information Theory are shown to be special cases of this general approach. Additionally, the approach allows the inclusion of prior partial knowledge of the desired solution and testing of various hypothesis concerning the solution characteristics. This work offers both new approaches to these problems as well as a theoretically sound general framework unifying the work of previous researchers. On a related problem, that of Blind Equalization for Digital Communication Channels, Dr. Noonan has derived a new solution utilizing the J-divergence functional of Information Theory. This technique offers improved Inter Symbol Interference (ISI) performance over existing techniques and has resulted in a patent. Other significant work involves new wavelet based estimation techniques for transient signals in noise and radar signal detection.

Dr. Noonan is currently continuing research on these areas with the objective of establishing as general a framework as possible for optimal estimation and detection under the umbrella of Information Theory. With ever increasing computational speed available, he is expanding these approaches to include more non-linear filtering and order statistics concepts. This new formulation is an effort to establish a more unified, robust and universal approach to the problems of estimation and system modeling.