  Using a multiplicative reparametrization, I show that a subclass of $L_q$
penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It
follows that the lasso and other norm-penalized regression estimates may be
obtained using a very simple and intuitive alternating ridge regression
algorithm. As compared to a similarly intuitive EM algorithm for $L_q$
optimization, the proposed algorithm avoids some numerical instability issues
and is also competitive in terms of speed. Furthermore, the proposed algorithm
can be extended to accommodate sparse high-dimensional scenarios, generalized
linear models, and can be used to create structured sparsity via penalties
derived from covariance models for the parameters. Such model-based penalties
may be useful for sparse estimation of spatially or temporally structured
parameters.
