Locally monotonic diffusion
Locally monotonic diffusion
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DOI：
10.1109/78.839984
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发表时间：
2000-05
期刊：
影响因子：
--
通讯作者：
Scott T. Acton
中科院分区：
文献类型：
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作者：
Scott T. Acton
各向异性扩散提供了一种有效的自适应信号平滑技术，可用于信号增强，信号分割和信号尺度空间创建。提出了一种基于偏微分方程（PDE）的局部单调信号扩散方法。不同于以前的扩散技术，发散或收敛到平凡的信号，局部单调（LOMO）扩散迅速收敛到定义良好的LOMO信号所需的程度。局部单调性的特性允许缓慢和快速的信号过渡（斜坡和阶跃边缘），同时排除由于噪声引起的离群值。与其他扩散方法相比，LOMO扩散不需要额外的正则化步骤来处理噪声信号，并且不使用自组织阈值或参数。在本文中，我们开发的LOMO扩散技术，并提供了几个显着的属性，包括稳定性和根信号的表征。与中值滤波器相比，该算法的收敛性良好（无振荡），且与信号长度无关。LOMO扩散的一个特殊情况与通过回归获得的最优解相同。实验结果验证了LOMO扩散可以产生去噪LOMO信号与低误差，使用更少的计算比中位数顺序统计方法。
Anisotropic diffusion affords an efficient, adaptive signal smoothing technique that can be used for signal enhancement, signal segmentation, and signal scale-space creation. This paper introduces a novel partial differential equation (PDE)-based diffusion method for generating locally monotonic signals. Unlike previous diffusion techniques that diverge or converge to trivial signals, locally monotonic (LOMO) diffusion converges rapidly to well-defined LOMO signals of the desired degree. The property of local monotonicity allows both slow and rapid signal transitions (ramp and step edges) while excluding outliers due to noise. In contrast with other diffusion methods, LOMO diffusion does not require an additional regularization step to process a noisy signal and uses no ad hoc thresholds or parameters. In the paper, we develop the LOMO diffusion technique and provide several salient properties, including stability and a characterization of the root signals. The convergence of the algorithm is well behaved (nonoscillatory) and is independent of the signal length, in contrast with the median filter. A special case of LOMO diffusion is identical to the optimal solution achieved via regression. Experimental results validate the claim that LOMO diffusion can produce denoised LOMO signals with low error using less computation than the median-order statistic approach.