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High resolution sparse estimation of exponentially decaying N-dimensional signals

Swärd, Johan LU ; Adalbjörnsson, Stefan I. LU and Jakobsson, Andreas LU (2016) In Signal Processing 128. p.309-317
Abstract

In this work, we consider the problem of high-resolution estimation of the parameters detailing an N-dimensional (N-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Since such signals are not sparse in an oversampled Fourier matrix, earlier approaches typically exploit large dictionary matrices that include not only a finely spaced frequency grid, but also a grid over the considered damping factors. Even in the 2-D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for N-dimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we... (More)

In this work, we consider the problem of high-resolution estimation of the parameters detailing an N-dimensional (N-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Since such signals are not sparse in an oversampled Fourier matrix, earlier approaches typically exploit large dictionary matrices that include not only a finely spaced frequency grid, but also a grid over the considered damping factors. Even in the 2-D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for N-dimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we introduce a novel dictionary learning approach that iteratively refines the estimate of the candidate frequency and damping coefficients for each component, thus allowing for smaller dictionaries, and for frequency and damping parameters that are not restricted to a grid. The performance of the proposed method is illustrated using simulated data, clearly showing the improved performance as compared to previous techniques.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Damped sinusoids, Dictionary learning, Parameter estimation, Sparse reconstruction, Sparse signal modeling, Spectral analysis
in
Signal Processing
volume
128
pages
9 pages
publisher
Elsevier
external identifiers
  • Scopus:84966392124
ISSN
0165-1684
DOI
10.1016/j.sigpro.2016.04.002
language
English
LU publication?
yes
id
8b1838fb-735d-47f5-9477-80533ca9da85
date added to LUP
2016-05-26 11:33:20
date last changed
2016-07-19 19:58:57
@misc{8b1838fb-735d-47f5-9477-80533ca9da85,
  abstract     = {<p>In this work, we consider the problem of high-resolution estimation of the parameters detailing an N-dimensional (N-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Since such signals are not sparse in an oversampled Fourier matrix, earlier approaches typically exploit large dictionary matrices that include not only a finely spaced frequency grid, but also a grid over the considered damping factors. Even in the 2-D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for N-dimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we introduce a novel dictionary learning approach that iteratively refines the estimate of the candidate frequency and damping coefficients for each component, thus allowing for smaller dictionaries, and for frequency and damping parameters that are not restricted to a grid. The performance of the proposed method is illustrated using simulated data, clearly showing the improved performance as compared to previous techniques.</p>},
  author       = {Swärd, Johan and Adalbjörnsson, Stefan I. and Jakobsson, Andreas},
  issn         = {0165-1684},
  keyword      = {Damped sinusoids,Dictionary learning,Parameter estimation,Sparse reconstruction,Sparse signal modeling,Spectral analysis},
  language     = {eng},
  month        = {11},
  pages        = {309--317},
  publisher    = {ARRAY(0x8adc880)},
  series       = {Signal Processing},
  title        = {High resolution sparse estimation of exponentially decaying N-dimensional signals},
  url          = {http://dx.doi.org/10.1016/j.sigpro.2016.04.002},
  volume       = {128},
  year         = {2016},
}