Open AccessNonconvex Energy Minimization with Unsupervised Line Process Classifier for Efficient Piecewise Constant Signals Reconstruction
Author(s) -
Anass Belcaid,
Mohammed Douimi
Publication year - 2021
Publication title -
statistics, optimization and information computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.297
H-Index - 12
eISSN - 2311-004X
pISSN - 2310-5070
DOI - 10.19139/soic-2310-5070-994
Subject(s) - piecewise , smoothing , computer science , step detection , algorithm , segmentation , filter (signal processing) , anomaly detection , artificial intelligence , pattern recognition (psychology) , probabilistic logic , noise reduction , minification , mathematical optimization , mathematics , computer vision , mathematical analysis
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 minimize the well-known line process model which arises from the probabilistic representation of the signal and its segmentation. In the first stage, we minimize a 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.