麻豆影院

Slepian Sequences and Subspace Models for Signal Processing Low-dimensional subspace models offer a convenient representation for many high-dimensional signals; such models form the backbone of least-squares signal processing and many common compression techniques. However, reconciling these subspace models with another fundamental signal processing tool--frequency analysis--can be difficult. For example, the popular discrete Fourier transform (DFT) will badly spread out the energy of even a simple sinusoid if its frequency does not fall on a regular grid. In this talk, we describe an alternative framework for developing subspace models based on a classical tool from time-frequency analysis: the Discrete Prolate Spheroidal Sequences, also known as the Slepian sequences. We review some basic--but remarkable--properties of Slepian sequences, discuss their effectiveness in building subspace models, present new results concerning an efficient dictionary constructed by concatenating Slepian sequences from multiple frequency bands, and discuss applications of these dictionaries in compressive sensing, radar imaging, and super-resolution. Bio: Michael B. Wakin is the Ben L. Fryrear Associate Professor in the Department of Electrical Engineering and Computer Science at the Colorado School of Mines (CSM). Dr. Wakin received a B.S. in electrical engineering and a B.A. in mathematics in 2000 (summa cum laude), an M.S. in electrical engineering in 2002, and a Ph.D. in electrical engineering in 2007, all from Rice University. He was an NSF Mathematical Sciences Postdoctoral Research Fellow at Caltech from 2006-2007 and an Assistant Professor at the University of Michigan from 2007-2008. His research interests include sparse, geometric, and manifold-based models for signal processing and compressive sensing. In 2007, Dr. Wakin shared the Hershel M. Rich Invention Award from Rice University for the design of a single-pixel camera based on compressive sensing; in 2008, Dr. Wakin received the DARPA Young Faculty Award for his research in compressive multi-signal processing for environments such as sensor and camera networks; in 2012, Dr. Wakin received the NSF CAREER Award for research into dimensionality reduction techniques for structured data sets; and in 2014, Dr. Wakin received the Excellence in Research Award for his research as a junior faculty member at CSM.