Sparse-regularized Least Squares and Nonlinear Smoothing

In this talk, we describe how certain signal smoothing problems can be formulated using sparse-regularized least squares. The L1 norm is often used for this purpose because it preserves the convexity of the objective function to be minimized. We describe novel non-convex regularizers that outperform the L1 norm, yet preserve the convexity of the objective function.