Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph

Jiang Yingchun; Li Ting

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Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph

机译：加权图上信号的局部测量和扩散重建

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Bandlimited graph signals on an unweighted graph can be reconstructed by its local measurement, which is a generalization of declination. Since most signals are weighted in real life, we extend and improve the iterative local measurement reconstruction (ILMR) by introducing the diffusion operators to reconstruct bandlimited signals on a weighted graph. We prove that the proposed reconstruction converges to the original signal. Moreover, the simulation results demonstrate that the improved algorithm has better convergence and has robustness against noise.

机译：未加权图上的带限图信号可以通过其局部测量来重建，这是磁偏角的一种概括。由于大多数信号在现实生活中都是经过加权的，因此我们通过引入扩散算子来重建加权图上的带宽受限信号，来扩展和改进迭代局部测量重建（ILMR）。我们证明了所提出的重构收敛于原始信号。仿真结果表明，改进算法具有较好的收敛性和鲁棒性。

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《Mathematical Problems in Engineering》 |2018年第9期|3264294.1-3264294.8|共8页
作者
Jiang Yingchun; Li Ting;
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Guangxi Coll & Univ Key Lab Data Anal & Computat, Guilin, Peoples R China;

Guilin Univ Elect Technol, Sch Math & Computat Sci, Guilin, Peoples R China;

Guangxi Key Lab Cryptog & Informat Secur, Guilin, Peoples R China;

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专利

1. Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph [J] . Yingchun Jiang, Ting Li Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第5期

机译：加权图上信号的局部测量和扩散重建
2. Diffusion-weighted MRI: Influence of intravoxel fat signal and breast density on breast tumor conspicuity and apparent diffusion coefficient measurements [J] . Partridge S.C., Singer L., Sun R., Magnetic resonance imaging: An International journal of basic research and clinical applications . 2011,第9期

机译：扩散加权MRI：体素内脂肪信号和乳房密度对乳腺肿瘤显眼性和表观扩散系数测量的影响
3. Value of diffusion-weighted MRI and apparent diffusion coefficient measurements for predicting the response of locally advanced rectal cancer to neoadjuvant chemoradiotherapy [J] . Iannicelli Elsa, Di Pietropaolo Marco, Pilozzi Emanuela, Abdominal radiology. . 2016,第10期

机译：弥散加权MRI和表观弥散系数测量对预测局部晚期直肠癌对新辅助放化疗的反应的价值
4. A CONTINUOUS MIXTURE OF TENSORS MODEL FOR DIFFUSION-WEIGHTED MR SIGNAL RECONSTRUCTION [C] . Bing Jian, Vemuri, B.C., . 2007

机译：弥散加权MR信号重建的张量模型的连续混合
5. Measurement and visualization of white matter fascicles using magnetic resonance diffusion-weighted imaging fiber tractography [D] . Sherbondy, Anthony 2008

机译：使用磁共振扩散加权成像纤维束成像技术测量和可视化白质纤维束
6. Diffusion-Weighted MRI: Influence of Intravoxel Fat Signal and Breast Density on Breast Tumor Conspicuity and Apparent Diffusion Coefficient Measurements [O] . Savannah C. Partridge, Lisa Singer, Ryan Sun, -1

机译：扩散加权MRI：透析脂肪信号和乳腺密度对乳腺肿瘤的影响和表观扩散系数测量
7. Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph [O] . Yingchun Jiang, Ting Li 2018

机译：对加权图中信号的局部测量和扩散重建

Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph

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