RIA: Optimum Multiresolution Analysis in Statistical Signal Processing

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The goals of this project are to: (1) study multiresolution approximations of nonstationary stochastic processes; (2) establish a novel framework for studying nonstationary signals, and (3) develop new analytic tools for addressing the related challenging problems of time-varying filtering, estimation, and coding. An optimal scaling function is proposed for "best" (in the mean- square sense) low-resolution approximation of a given process. Such an approximation is expected to improve the performance of filter banks used in subband coding for the efficient transmission of image or voice data. It will also lead to optimal feature extraction procedures in pattern recognition problems, appearing in underwater and remote sensing applications.