High-order total variation-based image restoration
High-order total variation-based image restoration
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DOI：
10.1137/s1064827598344169
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发表时间：
2000-08-31
影响因子：
3.1
通讯作者：
Mulet, P
中科院分区：
文献类型：
--
作者：
Chan, T;Marquina, A;Mulet, P
全变分(TV)去噪方法是一种基于偏微分方程的去噪方法，它很好地保留了边缘，但有时会产生不希望看到的阶梯效应，即将平滑区域(斜坡)转换为分段恒定区域(阶梯)。在本文中，我们提出了一个改进的模型，它是通过在变分TV模型的欧拉-拉格朗日方程中增加一个非线性四阶扩散项而构造的。我们的技术大大减少了楼梯效应，同时保留了尖锐的跳跃不连续(边缘)。在一维和二维数值算例中，我们给出了这种新模型相对于TV模型的分辨率的数值证据。
The total variation ( TV) denoising method is a PDE-based technique that preserves edges well but has the sometimes undesirable staircase effect, namely, the transformation of smooth regions ( ramps) into piecewise constant regions ( stairs). In this paper we present an improved model, constructed by adding a nonlinear fourth order diffusive term to the Euler-Lagrange equations of the variational TV model. Our technique substantially reduces the staircase effect, while preserving sharp jump discontinuities ( edges). We show numerical evidence of the power of resolution of this novel model with respect to the TV model in some 1D and 2D numerical examples.