Generalized Sparse Covariance-based Estimation

TL;DR

This paper generalizes the SPICE covariance estimator by incorporating different norm constraints, enhancing sparsity control, and providing new interpretations and solution methods, including grid-based and gridless approaches.

Contribution

The paper introduces a generalized SPICE method with norm-based constraints, offering improved sparsity control and alternative problem formulations with efficient solution techniques.

Findings

Extended SPICE allows for different norm constraints affecting sparsity.

The method is equivalent to a penalized regression problem, providing new insights.

Performance improvements over the original SPICE are demonstrated.

Abstract

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem.