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

TL;DR

This paper introduces advanced compressive parameter estimation algorithms utilizing polar interpolation for sparse translation-invariant signals, extending previous methods to complex amplitudes and mismatched manifolds, achieving improved accuracy at lower sampling rates.

Contribution

It extends polar interpolation-based estimation to complex amplitudes and mismatched manifolds, demonstrating improved precision and efficiency in sparse translation-invariant signal estimation.

Findings

Proposed algorithms outperform existing methods in estimation accuracy.

Using compressive sensing reduces sampling rate without sacrificing precision.

Algorithms offer tradeoffs between complexity, accuracy, and sampling requirements.

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.