  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. 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 l1-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.
