Compressive line spectrum estimation with clustering and interpolation

Abstract

We consider the standard line spectral estimation problem when the number of observed samples is significantly lower than that prescribed by the Nyquist rate. Two families of sparsity-based methods have recently been proposed for this problem. The first one uses an atomic norm minimization algorithm where the atoms correspond to complex exponentials of varying frequencies. The second one defines the sparse coefficient vectors for the signals of interest by designing parametric dictionaries that can be leveraged by sparse approximation algorithms involving clustering and interpolation. This paper compares the performance of these two algorithm families. Experiments show their advantages and disadvantages in terms of precision and complexity.

Compressive parameter estimation via K-median clustering

“…In order to test the performance of the clustering parameter estimation method on different problems, we present a number of numerical simulations involving time delay estimation and frequency estimation. 2 Before detailing our experimental setups, we define the parametric signals and the PDs involved in these two example applications. The parametric signal model for time delay estimation uses a chirp signal…”

“…$ Early versions of this work appeared at Proceedings of SPIE Wavelets and Sparsity XV, August 2013 [1] and 2016 Annual Conference on Information Science and Systems [2] Email addresses: mo@umass.edu (Dian Mo), mduarte@ecs.umass.edu (Marco F. Duarte) Recently, the application of CS has been extended from signal recovery to parameter estimation through the design of parametric dictionaries (PDs) that contain signal observations for a sampling set of the parameter space [6][7][8][9][10][11][12][13][14][15][16][17]. The resulting connection between parameter estimation and sparse signal recovery has made it possible for compressive parameter estimation to be implemented via standard CS recovery algorithms, where the PD coefficients obtained from recovery algorithms can be interpreted by matching the locations of the nonzero coefficients with the parameter estimates.…”