Weighted SPICE: A unifying approach for hyperparameter-free sparse estimation

In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA.1 Specifically, we show how the latter methods can be interpreted as variants of an adaptively reweighted SPICE method. Furthermore, we establish a connection between SPICE and the ℓ1ℓ1-penalized LAD estimator as well as the square-root LASSO method. We evaluate the four methods mentioned above in a generic sparse regression problem and in an array processing application.