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Fast Computations for Approximation and Compression in Slepian Spaces

Citation Author(s):
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport
Submitted by:
Santhosh Karnik
Last updated:
10 December 2016 - 2:11am
Document Type:
Presentation Slides
Document Year:
2016
Event:
Presenters:
Santhosh Karnik
Paper Code:
SSPC-1.3
 

The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for signals that are perfectly timelimited and nearly bandlimited. Unfortunately, because of the high computational complexity of projecting onto the DPSS basis -- also known as the Slepian basis -- this representation is often overlooked in favor of the fast Fourier transform (FFT). In this presentation, we show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desired approximation is increased. We demonstrate how these algorithms allow us to efficiently compute the solution to certain least-squares problems that arise in signal processing.

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