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Generalized sparse covariance-based estimation

Swärd, Johan LU ; Adalbjörnsson, Stefan I. LU and Jakobsson, Andreas LU (2018) In Signal Processing 143. p.311-319
Abstract

In this work, we generalize the recent sparse iterative covariance-based estimator (SPICE) by extending the problem formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. The resulting extended SPICE algorithm offers the same benefits as the regular SPICE algorithm, including being hyper-parameter free, but the choice of norms allows further control of the sparsity in the resulting solution. We also show that the proposed extension is equivalent to solving a penalized regression problem, providing further insight into the differences between the extended and original SPICE formulations. The performance of the method is evaluated for different choices of norms, indicating the... (More)

In this work, we generalize the recent sparse iterative covariance-based estimator (SPICE) by extending the problem formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. The resulting extended SPICE algorithm offers the same benefits as the regular SPICE algorithm, including being hyper-parameter free, but the choice of norms allows further control of the sparsity in the resulting solution. We also show that the proposed extension is equivalent to solving a penalized regression problem, providing further insight into the differences between the extended and original SPICE formulations. The performance of the method is evaluated for different choices of norms, indicating the preferable performance of the extended formulation as compared to the original SPICE algorithm. Finally, we introduce two implementations of the proposed algorithm, one gridless formulating for the sinusoidal case, resulting in a semi-definite programming problem, and one grid-based, for which an efficient implementation is given.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convex optimization, Covariance fitting, Sparse reconstruction
in
Signal Processing
volume
143
pages
9 pages
publisher
Elsevier
external identifiers
  • scopus:85029722145
ISSN
0165-1684
DOI
10.1016/j.sigpro.2017.09.010
language
English
LU publication?
yes
id
85f875c6-4594-44b9-98fa-8eee17fd8d22
date added to LUP
2017-10-05 10:50:41
date last changed
2018-01-07 12:20:45
@article{85f875c6-4594-44b9-98fa-8eee17fd8d22,
  abstract     = {<p>In this work, we generalize the recent sparse iterative covariance-based estimator (SPICE) by extending the problem formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. The resulting extended SPICE algorithm offers the same benefits as the regular SPICE algorithm, including being hyper-parameter free, but the choice of norms allows further control of the sparsity in the resulting solution. We also show that the proposed extension is equivalent to solving a penalized regression problem, providing further insight into the differences between the extended and original SPICE formulations. The performance of the method is evaluated for different choices of norms, indicating the preferable performance of the extended formulation as compared to the original SPICE algorithm. Finally, we introduce two implementations of the proposed algorithm, one gridless formulating for the sinusoidal case, resulting in a semi-definite programming problem, and one grid-based, for which an efficient implementation is given.</p>},
  author       = {Swärd, Johan and Adalbjörnsson, Stefan I. and Jakobsson, Andreas},
  issn         = {0165-1684},
  keyword      = {Convex optimization,Covariance fitting,Sparse reconstruction},
  language     = {eng},
  month        = {02},
  pages        = {311--319},
  publisher    = {Elsevier},
  series       = {Signal Processing},
  title        = {Generalized sparse covariance-based estimation},
  url          = {http://dx.doi.org/10.1016/j.sigpro.2017.09.010},
  volume       = {143},
  year         = {2018},
}