A homotopy recursive-in-model-order algorithm for weighted Lasso

A fast algorithm to solve weighted ℓ₁-minimization problems with N × N square “measuring” matrices is proposed. The method is recursive-in-model-order and tracks a homotopy path that goes through solutions of the optimization sub-tasks in the order of 1 through N. It thus yields solutions for all model orders and performs this task faster than the other compared methods. We show applications of this method in sparse linear system identification, in particular, the estimation of sparse target-cancellation filters for audio source separation.