Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

Karsten Fyhn, Marco F. Duarte, Søren Holdt Jensen

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

28 Citationer (Scopus)
571 Downloads (Pure)

Resumé

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.
OriginalsprogEngelsk
TidsskriftI E E E Transactions on Signal Processing
Vol/bind63
Udgave nummer4
Sider (fra-til)870-881
ISSN1053-587X
DOI
StatusUdgivet - 2015

Fingerprint

Parameter estimation
Interpolation
Sampling
Computational complexity
Frequency estimation
Time delay
Polynomials
Experiments

Citer dette

@article{56d35506d4ae42969a367ec95b1160c7,
title = "Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation",
abstract = "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.",
author = "Karsten Fyhn and Duarte, {Marco F.} and Jensen, {S{\o}ren Holdt}",
year = "2015",
doi = "10.1109/TSP.2014.2385035",
language = "English",
volume = "63",
pages = "870--881",
journal = "I E E E Transactions on Signal Processing",
issn = "1053-587X",
publisher = "IEEE",
number = "4",

}

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation. / Fyhn, Karsten; Duarte, Marco F. ; Jensen, Søren Holdt.

I: I E E E Transactions on Signal Processing, Bind 63, Nr. 4, 2015, s. 870-881.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

AU - Fyhn, Karsten

AU - Duarte, Marco F.

AU - Jensen, Søren Holdt

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

U2 - 10.1109/TSP.2014.2385035

DO - 10.1109/TSP.2014.2385035

M3 - Journal article

VL - 63

SP - 870

EP - 881

JO - I E E E Transactions on Signal Processing

JF - I E E E Transactions on Signal Processing

SN - 1053-587X

IS - 4

ER -