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A NOTE ON SINGULAR VALUE DECOMPOSITION FOR radon transform IN R^n

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Acta Mathematica Scientia 2002年第3期22卷 311-318页

作者：王金平杜金元 School of Mathematics and Statistics Wuhan University Wuhan 430072 China Department of Mathematics Hubei Normal University Huangshi 435002 China

The singular value decomposition is derived when the radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.

关键词： radon transform projection-slice theorem singular value decomposition

Wavelet transform and radon transform on the Quaternion Heisenberg Group

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Acta Mathematica Sinica,English Series 2014年第4期30卷 619-636页

作者： Jian Xun HE He Ping LIU School of Mathematics and Information Sciences Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University LMAM School of Mathematical SciencesPeking University

Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2（）. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the radon transform is a bijection. We deal with the radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the radon transform associated with the sub-Laplacian on .

关键词： Quaternion Heisenberg group wavelet transform radon transform inverse radon transform

radon CLF:A Novel Approach for Skew Detection Using radon transform

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Computer Systems Science & Engineering 2023年第10期47卷 675-697页

作者： Yuhang Chen Mahdi Bahaghighat Aghil Esmaeili Kelishomi Jingyi Du Laboratory for Control Engineering Xi’an University of Science&TechnologyXi’anChina Computer Engineering Department Imam Khomeini International UniversityQazvinIran MOE Key Laboratory for Intelligent and Network Security Xi’an Jiaotong UniversityXi’anChina

In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the radon transform and Curve Length Fitness Function(CLF),so-called radon CLF,was proposed.The radon CLF model aims to take advantage of the properties of radon spaces.The radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.

关键词： Document image analysis skew detection radon transform pattern recognition

INVERSE radon transform WITH ONE-DIMENSIONAL WAVELET transform

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Acta Mathematicae Applicatae Sinica 2000年第1期16卷 70-77页

作者：渠刚荣 Science College Northern Jiaotong University Beijing China

In this paper, the wavelet inverse formula of radon transform is obtained with onedimensional wavelet. The convolution back-projection method of radon transform is derived from this inverse formula. An asymptotic relation between wavelet inverse formula of radon transform and convolution-back projection algorithm of radon transform in 2 dimensions is established.

关键词： radon transform wavelet transform wavelet inversion formula convolution back-projection method

Auto detection of wood texture orientation by radon transform

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Journal of Forestry Research 2005年第1期16卷 1-4,i001页

作者： YUHai-peng LIUYi-xing LIUZhen-bo KeyLaboratoryofBio-basedMaterialScienceandTechnology（NortheastForestryUniversity） MinistryofEducationHarbin150040P.R.China

A novel and efficient approach for detecting wood texture orientation by computer was presented. Four Matlab functions were tried to describe the relative position and orientation of wood texture pixels, to detect texture shape and to create skeletal lines image of wood texture, and BWMORPH function was found the best one. Then by radon transform, it generated a signature composed of 180 values, each value summing up the size of texture lines that are shaped along that angle, and a two dimensional curve plot was drawn to represent the texture orientation of wood. Furthermore, it analyzed texture orientations of forty species as well as their general statistic laws, classified by softwood, hardwood, radial section and tangential section, and the results showed that texture orientation laws described by radon trans- form plot and their extracting datum were in accord with the impression of wood texture that people possessed in daily life, which con- firmed the validity of this new approach and their appealing utilization potentials.

关键词： Wood Texture Orientation radon transform Digital image processing

The radon transform on Tangent Space of Bounded Symmetric Domain SO~*(8)/U(4)

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Wuhan University Journal of Natural Sciences 1997年第4期2卷 12-22页

作者： Zhu Fuliu Department of Mathematics, Wuhan University, Wuhan 430072, China

We study the radon transform on the Cartan motion group associated with the bounded symmetric domain SO * (8)/U(4) , and prove that certain orbit of the regular elements is not the spectral synthesis set for th... 详细信息

关键词： radon transform hyperbolic equation spectral synthesis

Ship Wakes Detection in SAR Images Based on the Joint radon transform and Entropy

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Ship Wakes Detection in SAR Images Based on the Joint Radon ...

Method of Blob Detection Based on radon transform

2006 CIE International Conference on Radar

作者： Pengfei Du Ziyue Tang Yongliang Wang Yongjian Sun Wuhan Radar Academy Wuhan 430029 China

In order to distinguish true ship wakes from other spurious linear feature effectively,a novel method of ship wakes detection based on the radon transform （RT） and on the entropy,and named joint radon and entropy detection algorithm （JRE） is proposed.The proposed approach extracts all possible peaks in radon transform space with a low threshold,then computes the entropies centering around each peak and identifies the true ship wakes from spurious ones.Furthermore,the method can increase the detection probability and reduce the false alarm probability.Theoretical analysis and experimental results show that the method is capable of detecting synthetic aperture radar （SAR） ship wakes precisely and reliably in the presence of both strong noise and sea clutter.

关键词： SAR images ship wakes radon transform entropy

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Method of Blob Detection Based on Radon Transform

Multiple attenuation:An approach by incorporating multiple prediction with the radon transform

第30届中国控制与决策会议

作者： Cheng Chen Qipeng Chen Chang Gao Nan Zhang Xuguang Wang Yongjie Zhai Power Systems Artificial Intelligence Joint Laboratory of SGCC Global Energy Interconnection Research Institute co. Ltd School of Control and Computer Engineering North China Electric Power University

Blob has been widely used in image matching, target identification, and target tracking, etc., which makes efficient Blob detection a fundamental research subject in computer vision applications. Inspired by radon transform and taking the geometric characteristics of Blob into account, a Blob detection method is proposed in this paper. Firstly,a definition of the Blob response function is given, which is used to implement the statistics of intensity variations along the edges on both sides of the Blob. Then taking the calculated function value as the energy of the Blob center, the Blob is extracted by comparing the empirical threshold with the function value. Some experiments are carried out, and the results indicate that the proposed method can not only locate the position of Blobs with speed and accuracy, but also possess a good robustness to noises.

关键词： feature point Blob feature detection radon transform

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Multiple attenuation:An approach by incorporating multiple p...