A DPS filter for nonconvex edge preserving for PieceWise constant signals denoising

A robust estimator, namely the DPS algorithm, for piecewise constant signals denoising, is revised in this paper. Starting from its Markov random field formulation, which defines the solution as the global minimizer of a non-convex non-smooth energy function. The DPS algorithm transforms the line process mixed energy into a discrete optimization problem and proposes a BFS search strategy to find the optimal state. We develop a numerical scheme to replace the BFS search by a simple linear scan over the edges of the MRF. Each visit to an edge considers a local blanket of the MRF and then computes the estimated signal around the vicinity of the edge. The gradient of the solution will decide the existence or absence of a discontinuity based on a threshold. Theoretical results shows that the new implementation has a linear time and space complexity, but the local aspect reduces the robustness of the method against noise. A set of numerical simulations assist to show the reduction in time compared to the classical implementation and to compare the restoration quality against state-of-the-art algorithms.