  So-called sparse estimators arise in the context of model fitting, when one a
priori assumes that only a few (unknown) model parameters deviate from zero.
Sparsity constraints can be useful when the estimation problem is
under-determined, i.e. when number of model parameters is much higher than the
number of data points. Typically, such constraints are enforced by minimizing
the L1 norm, which yields the so-called LASSO estimator. In this work, we
propose a simple parameter transform that emulates sparse priors without
sacrificing the simplicity and robustness of L2-norm regularization schemes. We
show how L1 regularization can be obtained with a "sparsify" remapping of
parameters under normal Bayesian priors, and we demonstrate the ensuing
variational Laplace approach using Monte-Carlo simulations.
