Functional denoising and reconstruction of fractal imagesequences

M. D. Ruiz-Medina; N. N. Leonenko

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Functional denoising and reconstruction of fractal imagesequences

机译：分形图像序列的功能降噪和重建

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Fractal Gaussian models play a crucial role in image analysis applications (e.g.biophysics, geophysics, medical imaging data). In this paper, the filtering and reconstruc-tion problems for noisy and blurred homogeneous and heterogeneous fractal functional imagesequence data are studied. Specifically, conditions under which a stable solution to these prob-lems is obtained are derived by applying spectral and perturbation theories for fractal andmultifractional pseudodifferential operators. Numerical examples are provided to illustrate theobtained results.

机译：分形高斯模型在图像分析应用程序（例如生物物理学，地球物理学，医学成像数据）中起着至关重要的作用。本文研究了噪声和模糊的均质和异质分形功能图像序列数据的滤波和重构问题。具体来说，通过应用针对分形和多分式伪微分算子的谱和微扰理论，得出可以稳定解决这些问题的条件。数值例子说明了所获得的结果。

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《Random operators and stochastic equations》 |2009年第3期|共19页
作者
M. D. Ruiz-Medina; N. N. Leonenko;
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正文语种 eng
中图分类随机微分方程;
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Fractal processes; functional data; perturbation theory; pseudodifferential opera-tors; strong spatial dependence;

机译：分形过程;功能数据;摄动理论;伪微分算子;强空间依赖性;

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1. Functional denoising and reconstruction of fractal imagesequences [J] . M. D. Ruiz-Medina, N. N. Leonenko Random operators and stochastic equations . 2009,第3期

机译：分形图像序列的功能降噪和重建
2. Multiple CT-reconstructions for locally adaptive anisotropic wavelet denoising [J] . Anja Borsdorf, Rainer Raupach, Joachim Hornegger International Journal of Computer Assisted Radiology and Surgery . 2008,第5期

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3. Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part I: theory [J] . Guleryuz O.G. IEEE Transactions on Image Processing . 2006,第3期

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4. A conditional random field model for 3D Reconstruction in imagesequences [C] . Zhang Dazhi, Gong Junbin, Wang Yongtao International Symposium on Multispectral Image Processing and Pattern Recognition . 2009

机译：ImageSequences中三维重建的条件随机场模型
5. Signal Estimation by Superposition Modeling With Applications to Dynamic MRI Reconstruction, Hyperspectral Image Denoising, Light Detection in Viirs Data and Biosensor Data Denoising [D] . Yin, Lei. 2019

机译：通过应用于动态MRI重建的叠加建模，高光谱图像去噪，VIIRS数据和生物传感器数据去噪中的光检测信号估计
6. On fractality of functional near-infrared spectroscopy signals: analysis and applications [O] . Li Zhu, Sasan Haghani, Laleh Najafizadeh 2020

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7. Non-local mean denoising using multiple PET reconstructions [O] . Hossein Arabi, Habib Zaidi 2020

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Functional denoising and reconstruction of fractal imagesequences

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