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ISyE Statistics Seminar: A novel methodology for effective wavelet constructions in high dimensions
GUEST LECTURER
Youngmi Hur
AFFILIATION
Assistant Professor, Department of Applied mathematics and Statistics, Johns Hopkins University; and C.L.E. Moor Instructor, Department of Mathematics, MIT
ABSTRACT
We will start with an overview of the wavelet representation along with its applications to image processing. We will then discuss its connection with pyramidal representations such as the Laplacian, and some of existing challenges in constructing the wavelet/pyramidal representations in high dimensions.
Next, we will describe a new methodology for representing data on regular grids, which is a hybrid of the wavelet and the pyramidal representations. We will present the details of a subclass of these representations, dubbed L-CAMP. The L-CAMP methodology provides effective wavelet constructions in high dimensions in the sense that it has fast algorithms (linear complexity with small constants) for both decomposition and reconstruction, its performance (i.e., its ability to encode smoothness of an underlying data or function) is completely understood, and its localness number (measured as the sum of the volumes of the supports of the underlying mother wavelets) is extremely small.
