High resolution sparse estimation of exponentially decaying Ndimensional signals
(2016) In Signal Processing 128. p.309317 Abstract
In this work, we consider the problem of highresolution estimation of the parameters detailing an Ndimensional (ND) 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 2D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for Ndimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we... (More)
In this work, we consider the problem of highresolution estimation of the parameters detailing an Ndimensional (ND) 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 2D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for Ndimensional 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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 author
 Swärd, Johan ^{LU} ; Adalbjörnsson, Stefan I. ^{LU} and Jakobsson, Andreas ^{LU}
 organization
 publishing date
 20161101
 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
 01651684
 DOI
 10.1016/j.sigpro.2016.04.002
 language
 English
 LU publication?
 yes
 id
 8b1838fb735d47f5947780533ca9da85
 date added to LUP
 20160526 11:33:20
 date last changed
 20160719 19:58:57
@misc{8b1838fb735d47f5947780533ca9da85, abstract = {<p>In this work, we consider the problem of highresolution estimation of the parameters detailing an Ndimensional (ND) 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 2D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for Ndimensional 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 = {01651684}, keyword = {Damped sinusoids,Dictionary learning,Parameter estimation,Sparse reconstruction,Sparse signal modeling,Spectral analysis}, language = {eng}, month = {11}, pages = {309317}, publisher = {ARRAY(0x8adc880)}, series = {Signal Processing}, title = {High resolution sparse estimation of exponentially decaying Ndimensional signals}, url = {http://dx.doi.org/10.1016/j.sigpro.2016.04.002}, volume = {128}, year = {2016}, }