The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-bac...The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-backprojection (FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional (3D) local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography (ATRACT), not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.展开更多
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...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.展开更多
The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional ...The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional reconstruction method for the precession warhead via the micro-Doppler analysis and inverse Radon transform(IRT) is proposed in this paper. The precession parameters are extracted by the micro-Doppler analysis from three radars, and the IRT is used to estimate the size of targe. The scatterers of the target can be reconstructed based on the above parameters. Simulation experimental results illustrate the effectiveness of the proposed method in this paper.展开更多
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 tex...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.展开更多
In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography (SPECT) with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entai...In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography (SPECT) with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov's inversion operator into three parts bounded in the L2 sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to L(L^2(B). Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method.展开更多
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 ...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.展开更多
The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads...The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.展开更多
This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ (x') propagates th...This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ (x') propagates through an optical [D (-B) (-C) A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction ...The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transf...The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distributi...The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.展开更多
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...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 the Fourier algebra on this Cartan motion group.展开更多
<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information tr...<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary <em><strong>A</strong></em> = <em><strong>B</strong></em> = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc. </div>展开更多
Multiple prediction and subtraction techniques based on wavefield extrapolation are effective for suppressing multiple related to water layers. In the conventional wavefield extrapolation method,the multiples of the s...Multiple prediction and subtraction techniques based on wavefield extrapolation are effective for suppressing multiple related to water layers. In the conventional wavefield extrapolation method,the multiples of the seismic data are predicted from the known total wave field by the Green function convoluted with each point of the bottom. However,only the energy near the stationary phase point has an effect on the summation result when the convolutional gathers are added. The research proposed a stationary phase point extraction method based on high-resolution radon transform. In the radon domain,the energy near the stationary phase point is directly added along the convolutional gathers curve,which is a valid solution to the problem of the unstable phase of the events of multiple. The Curvelet matching subtraction technique is used to remove the multiple,which improved the accuracy of the multiple predicted by the wavefield extrapolation and the artifacts appearing around the events of multiple are well eliminated. The validity and feasibility of the proposed method are verified by the theoretical and practical data example.展开更多
In this article, we study reconstruction of nonuniform attenuated SPECT data and present analytic reconstruction formulae which are similar to Novikov's inversion formula. Furthermore, we extend Natterer's results.
Reflection imaging results generally reveal large-scale continuous geological information,and it is difficult to identify small-scale geological bodies such as breakpoints,pinch points,small fault blocks,caves,and fra...Reflection imaging results generally reveal large-scale continuous geological information,and it is difficult to identify small-scale geological bodies such as breakpoints,pinch points,small fault blocks,caves,and fractures,etc.Diffraction imaging is an important method to identify small-scale geological bodies and it has higher resolution than reflection imaging.In the common-offset domain,reflections are mostly expressed as smooth linear events,whereas diffractions are characterized by hyperbolic events.This paper proposes a diffraction extraction method based on double sparse transforms.The linear events can be sparsely expressed by the high-resolution linear Radon transform,and the curved events can be sparsely expressed by the Curvelet transform.A sparse inversion model is built and the alternating direction method is used to solve the inversion model.Simulation data and field data experimental results proved that the diffractions extraction method based on double sparse transforms can effectively improve the imaging quality of faults and other small-scale geological bodies.展开更多
Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-...Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.展开更多
In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivati...In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application.展开更多
A method used for recognition and understanding of airfield based on mathematical morphology is proposed in this paper. The new approach can he divided into three steps. First, to extract the typical geometric structu...A method used for recognition and understanding of airfield based on mathematical morphology is proposed in this paper. The new approach can he divided into three steps. First, to extract the typical geometric structure features of airfield, a segmentation method called recursive Otsu algorithm is employed on an airfield image. Second, thinning and shrinking algorithms are utilized to obtain the contour of airfield with single pixel and to remove diffused small particles. Finally, Radon transform is adopted to extract two typical and important components, primary and secondary runways of airfield exactly. At the same time, region growing algorithm is exploited to get the other components such as parking apron and garages. The experimental results demonstrate that the proposed method gives good performance.展开更多
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603)
文摘The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-backprojection (FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional (3D) local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography (ATRACT), not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.
文摘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.
基金supported by the National Natural Science Foundation of China (61871146)the Fundamental Research Funds for the Central Universities (FRFCU5710093720)。
文摘The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional reconstruction method for the precession warhead via the micro-Doppler analysis and inverse Radon transform(IRT) is proposed in this paper. The precession parameters are extracted by the micro-Doppler analysis from three radars, and the IRT is used to estimate the size of targe. The scatterers of the target can be reconstructed based on the above parameters. Simulation experimental results illustrate the effectiveness of the proposed method in this paper.
文摘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.
基金supported by the National Natural Science Foundation of China(61271398)K.C.Wong Magna Fund in Ningbo University
文摘In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography (SPECT) with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov's inversion operator into three parts bounded in the L2 sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to L(L^2(B). Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method.
文摘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.
基金Supported by the National Natural Science F oundation of China( No.199710 6 4) ,Key Project of Science and Tech-nology of Hubei Province Education Com mittee
文摘The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ (x') propagates through an optical [D (-B) (-C) A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
基金Supported by the Foundation of the Ministry of Education of China and the Science Foundation of Wuhan University
文摘The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.
基金supported by the National Natural Science Foundation of China(61271398)K.C.Wong Magna Fund in Ningbo UniversityNatural Science Foundation of Ningbo City(2010A610102)
文摘The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金supported by National Natural Science Foundation of China (Grant No 10874174)the President Foundation of Chinese Academy of Sciences
文摘The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.
文摘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 the Fourier algebra on this Cartan motion group.
文摘<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary <em><strong>A</strong></em> = <em><strong>B</strong></em> = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc. </div>
基金Supported by the National Science and Technology Major Project(No.2016ZX05026-002-003)the National Natural Science Foundation of China(No.41374108)
文摘Multiple prediction and subtraction techniques based on wavefield extrapolation are effective for suppressing multiple related to water layers. In the conventional wavefield extrapolation method,the multiples of the seismic data are predicted from the known total wave field by the Green function convoluted with each point of the bottom. However,only the energy near the stationary phase point has an effect on the summation result when the convolutional gathers are added. The research proposed a stationary phase point extraction method based on high-resolution radon transform. In the radon domain,the energy near the stationary phase point is directly added along the convolutional gathers curve,which is a valid solution to the problem of the unstable phase of the events of multiple. The Curvelet matching subtraction technique is used to remove the multiple,which improved the accuracy of the multiple predicted by the wavefield extrapolation and the artifacts appearing around the events of multiple are well eliminated. The validity and feasibility of the proposed method are verified by the theoretical and practical data example.
基金supported by the National Natural Science Foundation of China(61271398)Natural Science Foundation of Zhejiang Province(LY14A010004)K.C.Wong Magna Fund in Ningbo University
文摘In this article, we study reconstruction of nonuniform attenuated SPECT data and present analytic reconstruction formulae which are similar to Novikov's inversion formula. Furthermore, we extend Natterer's results.
基金supported by National Natural Science Foundation of China(41974166)Natural Science Foundation of Hebei Province(D2019403082,D2021403010)+1 种基金Hebei Province“three-threethree talent project”(A202005009)Funding for the Science and Technology Innovation Team Project of Hebei GEO University(KJCXTD202106)
文摘Reflection imaging results generally reveal large-scale continuous geological information,and it is difficult to identify small-scale geological bodies such as breakpoints,pinch points,small fault blocks,caves,and fractures,etc.Diffraction imaging is an important method to identify small-scale geological bodies and it has higher resolution than reflection imaging.In the common-offset domain,reflections are mostly expressed as smooth linear events,whereas diffractions are characterized by hyperbolic events.This paper proposes a diffraction extraction method based on double sparse transforms.The linear events can be sparsely expressed by the high-resolution linear Radon transform,and the curved events can be sparsely expressed by the Curvelet transform.A sparse inversion model is built and the alternating direction method is used to solve the inversion model.Simulation data and field data experimental results proved that the diffractions extraction method based on double sparse transforms can effectively improve the imaging quality of faults and other small-scale geological bodies.
基金supported by the National Natural Science Foundation of China (Nos. 10732100, 10572155)the Science and Technology Planning Project of Guangdong Province of China (No. 2006A11001002)the Ph. D. Programs Foundation of Ministry of Education of China (No. 2006300004111179)
文摘Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.
文摘In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application.
文摘A method used for recognition and understanding of airfield based on mathematical morphology is proposed in this paper. The new approach can he divided into three steps. First, to extract the typical geometric structure features of airfield, a segmentation method called recursive Otsu algorithm is employed on an airfield image. Second, thinning and shrinking algorithms are utilized to obtain the contour of airfield with single pixel and to remove diffused small particles. Finally, Radon transform is adopted to extract two typical and important components, primary and secondary runways of airfield exactly. At the same time, region growing algorithm is exploited to get the other components such as parking apron and garages. The experimental results demonstrate that the proposed method gives good performance.