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Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
IEEE Transactions on Signal Processing (2015)
  • Karsten Fyhn, Aalborg University
  • Marco Duarte, University of Massachusetts - Amherst
  • Søren Holdt Jensen, Aalborg University
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.
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This is the post-print version harvested from arXiv. The published version is located at DOI: 10.1109/TSP.2014.2385035 (c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Citation Information
Karsten Fyhn, Marco Duarte and Søren Holdt Jensen. "Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation" IEEE Transactions on Signal Processing Vol. 63 Iss. 4 (2015)
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