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Estimating Sparse Signals Using Integrated Wideband Dictionaries

Butsenko, Maksim; Svard, Johan LU and Jakobsson, Andreas LU (2018) In IEEE Transactions on Signal Processing 66(16). p.4170-4181
Abstract

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard... (More)

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Computational complexity, Dictionaries, Estimation, Frequency estimation, Optimization, Tensile stress, Wideband
in
IEEE Transactions on Signal Processing
volume
66
issue
16
pages
4170 - 4181
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85046995999
ISSN
1053-587X
DOI
10.1109/TSP.2018.2835426
language
English
LU publication?
yes
id
4d3c68e0-df2a-4f8c-88e5-a23f5b7de14e
date added to LUP
2018-05-30 13:19:21
date last changed
2019-01-14 15:52:35
@article{4d3c68e0-df2a-4f8c-88e5-a23f5b7de14e,
  abstract     = {<p>In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance.</p>},
  author       = {Butsenko, Maksim and Svard, Johan and Jakobsson, Andreas},
  issn         = {1053-587X},
  keyword      = {Computational complexity,Dictionaries,Estimation,Frequency estimation,Optimization,Tensile stress,Wideband},
  language     = {eng},
  month        = {05},
  number       = {16},
  pages        = {4170--4181},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Estimating Sparse Signals Using Integrated Wideband Dictionaries},
  url          = {http://dx.doi.org/10.1109/TSP.2018.2835426},
  volume       = {66},
  year         = {2018},
}