Piecewise-Polynomial signal segmentation using reweighted convex optimization

We present a method for segmenting a one-dimensional piecewise polynomial signal corrupted by an additive noise. The method's principal part is based on sparse modeling, and its formulation as a reweighted convex optimization problem is solved numerically by proximal splitting. The method solves a sequence of weighted l₂₁-minimization problems, where the weights used for the next iteration are computed from the current solution. We perform experiments on simulated and real data and discuss the results.