Modeling and processing of high dimensional signals and systems using the sparse matrix transform

Guangzhi Cao, Purdue University

Abstract

In this work, a set of new tools is developed for modeling and processing of high dimensional signals and systems, which we refer to as the sparse matrix transform (SMT). The SMT can be viewed as a generalization of the FFT and wavelet transforms in that it uses "butterflies" for efficient implementation. However, unlike the FFT and wavelet transforms, the design of the SMT is adapted to data, and therefore it can be used to process more general non-stationary signals. To demonstrate the potential of the SMT, it is first shown how the non-iterative maximum a posteriori (MAP) reconstruction can be made possible for tomographic systems using the SMT and a novel matrix source coding theory. In fact, for a class of difficult optical tomography problems, this non-iterative MAP reconstruction can reduce both computation and storage by well over two orders of magnitude. The SMT can also be used for accurate covariance estimation of high dimensional data vectors from a limited number of samples ("small n, large p"). Experiments on standard hyperspectral data and face image sets show that the SMT covariance estimation is consistently more accurate than alternative methods. This has also resulted in successful applications of the SMT for weak signal detection in hyperspectral imagery and eigen-image analysis. This work is concluded with a novel approach to high dimensional regression using the SMT, and it is demonstrated that the new approach can significantly improve prediction accuracy as compared to traditional regression methods.

Degree

Ph.D.

Advisors

Webb, Purdue University.

Subject Area

Electrical engineering

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