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.
(Less)
- author
- Swärd, Johan
LU
; Adalbjörnsson, Stefan I.
LU
and Jakobsson, Andreas
LU
- organization
- publishing date
- 2016-11-01
- 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
-
- wos:000379706500030
- 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
- 2024-01-04 07:36:56
@article{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}},
keywords = {{Damped sinusoids; Dictionary learning; Parameter estimation; Sparse reconstruction; Sparse signal modeling; Spectral analysis}},
language = {{eng}},
month = {{11}},
pages = {{309--317}},
publisher = {{Elsevier}},
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}},
doi = {{10.1016/j.sigpro.2016.04.002}},
volume = {{128}},
year = {{2016}},
}