Graph Signal Denoising via Trilateral Filter on Graph Spectral Domain
Graph Signal Denoising via Trilateral Filter on Graph Spectral Domain
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DOI：
10.1109/tsipn.2016.2532464
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发表时间：
2016-06-01
影响因子：
3.2
通讯作者：
Tanaka, Yuichi
中科院分区：
文献类型：
--
作者：
Onuki, Masaki;Ono, Shunsuke;Tanaka, Yuichi
本文提出了一种在图谱域定义三边形滤波的图形信号去噪方法。最初的三边形滤波(TF)是一种依赖于数据的滤波方法，被广泛用于图像处理中的边缘保持平滑方法。然而，由于数据的依赖性，不能提供其频域表示。为了克服这一问题，我们建立了数据相关过滤器的图谱域表示，即谱图TF(SGTF)。这种表示使我们能够利用Tikhonov正则化来设计有效的图形信号去噪滤波器。此外，对于所提出的图去噪滤波器，我们提供了一种参数优化技术来搜索近似最小化均方误差w.r.t的正则化参数。感兴趣的未知图形信号。综合的实验结果验证了基于图形信号处理的图像和图形信号处理方法的有效性。
This paper presents a graph signal denoising method with the trilateral filter defined in the graph spectral domain. The original trilateral filter (TF) is a data-dependent filter that is widely used as an edge-preserving smoothing method for image processing. However, because of the data-dependency, one cannot provide its frequency domain representation. To overcome this problem, we establish the graph spectral domain representation of the data-dependent filter, i.e., a spectral graph TF (SGTF). This representation enables us to design an effective graph signal denoising filter with a Tikhonov regularization. Moreover, for the proposed graph denoising filter, we provide a parameter optimization technique to search for a regularization parameter that approximately minimizes the mean squared error w.r.t. the unknown graph signal of interest. Comprehensive experimental results validate our graph signal processing-based approach for images and graph signals.