Generalized sparse covariance-based estimation

Research output: Contribution to journalArticle

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 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.

Details

Authors
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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Signal Processing

Keywords

  • Convex optimization, Covariance fitting, Sparse reconstruction
Original languageEnglish
Pages (from-to)311-319
Number of pages9
JournalSignal Processing
Volume143
StatePublished - 2018 Feb 1
Peer-reviewedYes