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  • Computer Science
  • Mathematics


1 Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation Karsten Fyhn, Student Member, IEEE, Marco F. Duarte, Member, IEEE, and Søren Holdt Jensen, Senior Member, IEEE Abstract We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Moreover, 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. The proposed algorithms are based on polar interpolation and our numerical experiments show that they outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to an 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 lower sampling rate and that the use of polar interpolation increases the estimation precision. Index Terms Compressive sensing, translation-invariant signals, interpolation, time delay estimation. I. INTRODUCTION Compressive sensing (CS) is a technique to simultaneously acquire and reduce the dimensionality of sparse signals in a randomized fashion. More precisely, in the CS framework, a signal f ∈ CN is sampled by M linear measurements of the form y = Af , where A ∈ CM×N is a sensing matrix and M < N . In practice, the measurements are acquired in the presence of additive signal and measurement noise n and w, resp

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