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Non-convex Total Variation Regularization for Convex Denoising of Signals
Journal of Mathematical Imaging and Vision ( IF 2 ) Pub Date : 2020-01-11 , DOI: 10.1007/s10851-019-00937-5
Ivan Selesnick , Alessandro Lanza , Serena Morigi , Fiorella Sgallari

Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a ‘convex non-convex’ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising.

中文翻译:

用于信号去噪的非凸总变化正则化

总变化(TV)信号降噪是一种流行的非线性滤波方法,用于估计由加性白高斯噪声破坏的分段常数信号。遵循“凸非凸”策略,最近的论文介绍了用于信号去噪的非凸正则化器,该正则化器保留了将成本函数的凸度最小化的特征。在本文中,我们提出了一种非凸电视正则器,它使用了凸分析的概念来定义,统一,概括和改进了这些正则器。特别是,我们使用广义的Moreau包络,与通常的Moreau包络不同,它包含矩阵参数。我们描述了一种新颖的方法来设置矩阵参数,这对于实现我们展示的改进至关重要。另外,
更新日期:2020-01-11
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