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 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.
Highlights
The problem of removing noise from piecewise constant (PWC) signals occurs naturally in several fields of applied sciences like genomic [1, 2], nanotechnology [3], image analysis [4] and finance [5, 6]
This is reflected by the Root Mean Square Error (RMSE) as Discontinuity Position Sweep (DPS) get a lower RMSE compared to total variation (TV) denoiser
We present the results with a state of the art algorithm called Energy Based Scheme (EBS) used in the same paper [32]
Summary
The problem of removing noise from piecewise constant (PWC) signals occurs naturally in several fields of applied sciences like genomic [1, 2], nanotechnology [3], image analysis [4] and finance [5, 6]. The prior knowledge is incorporated either by the means of regularization [9, 10] or by the Markov Random Fields (MRF) [11, 12] framework Both of which lead to the minimization of an energy function in the form: E(u) = ∥u − y∥22 + λφ(u). We emphasize on the truncated quadratic interaction [12] V (up, uq) = min{α, (up − uq)2} which is equivalent to the Line Process (LP) introduced in [16] With this choice, the regularizer tem φ(u) is given as sum ov IP V (ui, ui+1) over binary cliques in the form of (i, i + 1): φ(u). The results show an efficient increase in time and gain in robustness in the case of extremely corrupted signals
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