  l1 reweighting algorithms are very popular in sparse signal recovery and
compressed sensing, since in the practice they have been observed to outperform
classical l1 methods. Nevertheless, the theoretical analysis of their
convergence is a critical point, and generally is limited to the convergence of
the functional to a local minimum or to subsequence convergence. In this
letter, we propose a new convergence analysis of a Lasso l1 reweighting method,
based on the observation that the algorithm is an alternated convex search for
a biconvex problem. Based on that, we are able to prove the numerical
convergence of the sequence of the iterates generated by the algorithm. This is
not yet the convergence of the sequence, but it is close enough for practical
and numerical purposes. Furthermore, we propose an alternative iterative soft
thresholding procedure, which is faster than the main algorithm.
