Nonconvex Energy Minimization with Unsupervised Line Process Classifier for Efficient Piecewise Constant Signals Reconstruction

Abstract

In this paper, we focus on the problem of signal smoothing and step-detection for piecewise constant signals. This problem is central to several applications such as human activity analysis, speech or image analysis and anomaly detection in genetics. We present a two-stage approach to approximate the well-known line process energy which arises from the probabilistic representation of the signal and its segmentation. In the first stage, we minimize a total variation (TV) least square problem to detect the majority of the continuous edges. In the second stage, we apply a combinatorial algorithm to filter all false jumps introduced by the TV solution. The performances of the proposed method were tested on several synthetic examples. In comparison to recent step-preserving denoising algorithms, the acceleration presents a superior speed and competitive step-detection quality.