Fused-MCP With Application to Signal Processing

Friedman et al. proposed the fused lasso signal approximator (FLSA) to denoise piecewise constant signals by penalizing the ℓ₁ differences between adjacent signal points. In this article, we propose a new method, referred to as the fused-MCP, by combining the minimax concave penalty (MCP) with the fusion penalty. The fused-MCP performs better than the FLSA in maintaining the profile of the original signal and preserving the edge structure. We show that, with a high probability, the fused-MCP selects the right change-points and has the oracle property, unlike the FLSA. We further show that the fused-MCP achieves the same l₂ error rate as the FLSA. We develop algorithms to solve fused-MCP problems, either by transforming them into MCP regression problems or by using an adjusted majorization-minimization algorithm. Simulation and experimental results show the effectiveness of our method. Supplementary material for this article is available online.