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Fast Computations for Approximation and Compression in Slepian Spaces

Abstract: 

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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Paper Details

Authors:
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport
Submitted On:
10 December 2016 - 2:11am
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Santhosh Karnik
Paper Code:
SSPC-1.3
Document Year:
2016
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Document Files

GlobalSIP2016SSPC13.pdf

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[1] Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport, "Fast Computations for Approximation and Compression in Slepian Spaces", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1436. Accessed: Aug. 19, 2017.
@article{1436-16,
url = {http://sigport.org/1436},
author = {Santhosh Karnik; Zhihui Zhu; Michael B. Wakin; Justin Romberg; Mark A. Davenport },
publisher = {IEEE SigPort},
title = {Fast Computations for Approximation and Compression in Slepian Spaces},
year = {2016} }
TY - EJOUR
T1 - Fast Computations for Approximation and Compression in Slepian Spaces
AU - Santhosh Karnik; Zhihui Zhu; Michael B. Wakin; Justin Romberg; Mark A. Davenport
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1436
ER -
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport. (2016). Fast Computations for Approximation and Compression in Slepian Spaces. IEEE SigPort. http://sigport.org/1436
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport, 2016. Fast Computations for Approximation and Compression in Slepian Spaces. Available at: http://sigport.org/1436.
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport. (2016). "Fast Computations for Approximation and Compression in Slepian Spaces." Web.
1. Santhosh Karnik, Zhihui Zhu, Michael B. Wakin, Justin Romberg, Mark A. Davenport. Fast Computations for Approximation and Compression in Slepian Spaces [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1436