A fast implementation of the convolution backprojection（CBP）algorithm in spotlight synthetic aperture radar（SAR）is presented based on the fast Fourier transform（FFT）.Traditionally,the computation of the ＇backpr...A fast implementation of the convolution backprojection（CBP）algorithm in spotlight synthetic aperture radar（SAR）is presented based on the fast Fourier transform（FFT）.Traditionally,the computation of the ＇backprojection＇ process is expensive,since resampling in the process is implemented by using the interpolation operation.By analyzing the relative location relationship among different pixels,the algorithm realizes the ＇backprojection＇ using a series of FFTs instead of the interpolation operation.The point target simulation validates that the new algorithm accelerates the CBP algorithm,and the computational rate increases about 85%.展开更多
Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-d...Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-domain backprojection with minimal loss in accuracy for straight-line motion. However, its implementation is not as straightforward as direct backprojection. This paper provides a new, easily parallelizable formulation of factorized backprojection designed for stripmap SAR data that includes a method of implementing an azimuth window as part of the factorized backprojection algorithm. We compare the performance of windowed factorized backprojection to direct backprojection for simulated and actual SAR data.展开更多
The distribution of incident angles of the discrete projection data may be uneven when the wave rays in random medium are nonlinear, moreover, the far field condition will be broken down when the inversion region is l...The distribution of incident angles of the discrete projection data may be uneven when the wave rays in random medium are nonlinear, moreover, the far field condition will be broken down when the inversion region is large. Thus the inversion result will be distorted unavoidably in many ray inversion methods. In order to eliminate these influences, a new t-x(time-spac) domain backprojection method compensating the density of the distribution of incident angles is developed. The paper provides the principle of the incident angle compensation and simulation result of a point defect in layered medium.展开更多
In this article we introduce an exact backprojection filtered (BPF) type reconstruction algorithm for cone-beam scans based on Zou and Pan’s work. The algorithm can reconstruct images using only the projection data p...In this article we introduce an exact backprojection filtered (BPF) type reconstruction algorithm for cone-beam scans based on Zou and Pan’s work. The algorithm can reconstruct images using only the projection data passing through the parallel PI-line segments in reduced scans. Computer simulations and practical experiments are carried out to evaluate this algorithm. The BPF algorithm has a higher computational efficiency than the famous FDK algorithm. The BPF algorithm is evaluated using the practical CT projection data on a 450 keV X-ray CT system with a flat-panel detector (FPD). From the practical experiments, we get the spatial resolution of this CT system. The algo- rithm could achieve the spatial resolution of 2.4 lp/mm and satisfies the practical applications in industrial CT inspec- tion.展开更多
In helical cone-beam computed tomography(CT), Feldkamp-Davis-Kress(FDK) based image reconstruction algorithms are by far the most popular. However, artifacts are commonly met in the presence of lateral projection trun...In helical cone-beam computed tomography(CT), Feldkamp-Davis-Kress(FDK) based image reconstruction algorithms are by far the most popular. However, artifacts are commonly met in the presence of lateral projection truncation. The reason is that the ramp filter is global. To restrain the truncation artifacts, an approximate reconstruction formula is proposed based on the Derivative-Hilbert-Backprojection(DHB) framework. In the method, the first order derivative filter is followed by the Hilbert transform. Since the filtered projection values are almost zero by the first order derivative filter, the following Hilbert transform has little influence on the projection values, even though the projections are laterally truncated. The proposed method has two main advantages. First, it has comparable computational efficiency and image quality as well as the conventional helical FDK algorithm for non-truncated projections. The second advantage is that images can be reconstructed with acceptable quality and much lower computational cost in comparison to the Laplace operator based algorithm in cases with truncated projections. To point out the advantages of our method, simulations on the computer and real data experiments on our laboratory industrial cone-beam CT are conducted. The simulated and experimental results demonstrate that the method is feasible for image reconstruction in the case of projection truncation.展开更多
The high radiation dose in computed tomography （CT） scans increases the lifetime risk of cancer, which becomes a major clinical concern. The backprojection-filtration （BPF） algorithm could reduce the radiation dos...The high radiation dose in computed tomography （CT） scans increases the lifetime risk of cancer, which becomes a major clinical concern. The backprojection-filtration （BPF） algorithm could reduce the radiation dose by reconstructing the images from truncated data in a short scan. In a dental CT, it could reduce the radiation dose for the teeth by using the projection acquired in a short scan, and could avoid irradiation to the other part by using truncated projection. However, the limit of integration for backprojection varies per PI-line, resulting in low calculation efficiency and poor parallel performance. Recently, a tent BPF has been proposed to improve the calculation efficiency by rearranging the projection. However, the memory-consuming data rebinning process is included. Accordingly, the selective BPF （S-BPF） algorithm is proposed in this paper. In this algorithm, the derivative of the projection is backprojected to the points whose x coordinate is less than that of the source focal spot to obtain the differentiated backprojection. The finite Hilbert inverse is then applied to each PI-line segment. S-BPF avoids the influence of the variable limit of integration by selective backprojection without additional time cost or memory cost. The simulation experiment and the real experiment demonstrated the higher reconstruction efficiency of S-BPF.展开更多
A direct filtered-backprojection （FBP） reconstruction algorithm is presented for circular cone-beam computed tomography （CB-CT） that allows the filter operation to be applied efficiently with shift-variant band-pa...A direct filtered-backprojection （FBP） reconstruction algorithm is presented for circular cone-beam computed tomography （CB-CT） that allows the filter operation to be applied efficiently with shift-variant band-pass characteristics on the kernel function. Our algorithm is derived from the ramp-filter based FBP method of Feldkamp et al. and obtained by decomposing the ramp filtering into a convolution involving the Hilbert kernel （global operation） and a subsequent differentiation operation （local operation）. The differentiation is implemented as a finite difference of two （Hilbert filtered） data samples and carried out as part of the backprojection step. The spacing between the two samples, which defines the low-pass characteristics of the filter operation, can thus be selected individually for each point in the image volume. We here define the sample spacing to follow the magnification of the divergent-beam geometry and thus obtain a novel, depth-dependent filtering algorithm for circular CB-CT. We evaluate this resulting algorithm using computer-simulated CB data and demonstrate that our algorithm yields results where spatial resolution and image noise are distributed much more uniformly over the field-of-view, compared to Feldkamp＇s approach.展开更多
Based on the geometrical relationships between image pixels and projection rays at different viewing angles,a Multiorientation Simultaneous Back Projection (MSBP) approach is proposed in this papar for two-dimensional...Based on the geometrical relationships between image pixels and projection rays at different viewing angles,a Multiorientation Simultaneous Back Projection (MSBP) approach is proposed in this papar for two-dimensional (2-D) parallel and fan beam CT systems. In this scheme, backprojections for eight views, 6, π/2 - θ, π/2 + 6, π- θ, π+ θ, 3π/2 - θ, 3π/2 + θ, and 2π- θ, are implemented at the same time,while the locating operation of pixels for interpolation and computation of weighting parameters are only required for one of them when one half of the number of thaws is even. Implementation remits on an Intel 80386 hosed computer show that the proposed method has a notable computational gain,compared with the conventional implementation of backprojection.展开更多
基金Supported by the National Natural Science Foundation of China(61071165)the Aeronautical Science Foundation of China(20080152004)+1 种基金the Ph.D.Programs Foundation of Ministry of Education of China(20070280531)the Program for New Century Excellent Talents in University(NCET-09-0069)~~
文摘A fast implementation of the convolution backprojection（CBP）algorithm in spotlight synthetic aperture radar（SAR）is presented based on the fast Fourier transform（FFT）.Traditionally,the computation of the ＇backprojection＇ process is expensive,since resampling in the process is implemented by using the interpolation operation.By analyzing the relative location relationship among different pixels,the algorithm realizes the ＇backprojection＇ using a series of FFTs instead of the interpolation operation.The point target simulation validates that the new algorithm accelerates the CBP algorithm,and the computational rate increases about 85%.
文摘Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-domain backprojection with minimal loss in accuracy for straight-line motion. However, its implementation is not as straightforward as direct backprojection. This paper provides a new, easily parallelizable formulation of factorized backprojection designed for stripmap SAR data that includes a method of implementing an azimuth window as part of the factorized backprojection algorithm. We compare the performance of windowed factorized backprojection to direct backprojection for simulated and actual SAR data.
文摘The distribution of incident angles of the discrete projection data may be uneven when the wave rays in random medium are nonlinear, moreover, the far field condition will be broken down when the inversion region is large. Thus the inversion result will be distorted unavoidably in many ray inversion methods. In order to eliminate these influences, a new t-x(time-spac) domain backprojection method compensating the density of the distribution of incident angles is developed. The paper provides the principle of the incident angle compensation and simulation result of a point defect in layered medium.
基金Supported by a grant from the Ph.D. Programs Foundation of Ministry of Education of China (No. 20030003074) and the National Natural Science Founda-tion of China (No. 10575059).
文摘In this article we introduce an exact backprojection filtered (BPF) type reconstruction algorithm for cone-beam scans based on Zou and Pan’s work. The algorithm can reconstruct images using only the projection data passing through the parallel PI-line segments in reduced scans. Computer simulations and practical experiments are carried out to evaluate this algorithm. The BPF algorithm has a higher computational efficiency than the famous FDK algorithm. The BPF algorithm is evaluated using the practical CT projection data on a 450 keV X-ray CT system with a flat-panel detector (FPD). From the practical experiments, we get the spatial resolution of this CT system. The algo- rithm could achieve the spatial resolution of 2.4 lp/mm and satisfies the practical applications in industrial CT inspec- tion.
基金Supported by the National High Technology Research and Development Program of China(No.2012AA011603)National Nature Science Foundation of China(No.61372172)
文摘In helical cone-beam computed tomography(CT), Feldkamp-Davis-Kress(FDK) based image reconstruction algorithms are by far the most popular. However, artifacts are commonly met in the presence of lateral projection truncation. The reason is that the ramp filter is global. To restrain the truncation artifacts, an approximate reconstruction formula is proposed based on the Derivative-Hilbert-Backprojection(DHB) framework. In the method, the first order derivative filter is followed by the Hilbert transform. Since the filtered projection values are almost zero by the first order derivative filter, the following Hilbert transform has little influence on the projection values, even though the projections are laterally truncated. The proposed method has two main advantages. First, it has comparable computational efficiency and image quality as well as the conventional helical FDK algorithm for non-truncated projections. The second advantage is that images can be reconstructed with acceptable quality and much lower computational cost in comparison to the Laplace operator based algorithm in cases with truncated projections. To point out the advantages of our method, simulations on the computer and real data experiments on our laboratory industrial cone-beam CT are conducted. The simulated and experimental results demonstrate that the method is feasible for image reconstruction in the case of projection truncation.
基金Supported by National High Technology Research and Development Program of China(2012AA011603)National Natural Science Foundation of China(61372172)
文摘The high radiation dose in computed tomography （CT） scans increases the lifetime risk of cancer, which becomes a major clinical concern. The backprojection-filtration （BPF） algorithm could reduce the radiation dose by reconstructing the images from truncated data in a short scan. In a dental CT, it could reduce the radiation dose for the teeth by using the projection acquired in a short scan, and could avoid irradiation to the other part by using truncated projection. However, the limit of integration for backprojection varies per PI-line, resulting in low calculation efficiency and poor parallel performance. Recently, a tent BPF has been proposed to improve the calculation efficiency by rearranging the projection. However, the memory-consuming data rebinning process is included. Accordingly, the selective BPF （S-BPF） algorithm is proposed in this paper. In this algorithm, the derivative of the projection is backprojected to the points whose x coordinate is less than that of the source focal spot to obtain the differentiated backprojection. The finite Hilbert inverse is then applied to each PI-line segment. S-BPF avoids the influence of the variable limit of integration by selective backprojection without additional time cost or memory cost. The simulation experiment and the real experiment demonstrated the higher reconstruction efficiency of S-BPF.
基金Supported in part by the US National Institute of Health (Nos.R01EB007236 and R21EB009168)
文摘A direct filtered-backprojection （FBP） reconstruction algorithm is presented for circular cone-beam computed tomography （CB-CT） that allows the filter operation to be applied efficiently with shift-variant band-pass characteristics on the kernel function. Our algorithm is derived from the ramp-filter based FBP method of Feldkamp et al. and obtained by decomposing the ramp filtering into a convolution involving the Hilbert kernel （global operation） and a subsequent differentiation operation （local operation）. The differentiation is implemented as a finite difference of two （Hilbert filtered） data samples and carried out as part of the backprojection step. The spacing between the two samples, which defines the low-pass characteristics of the filter operation, can thus be selected individually for each point in the image volume. We here define the sample spacing to follow the magnification of the divergent-beam geometry and thus obtain a novel, depth-dependent filtering algorithm for circular CB-CT. We evaluate this resulting algorithm using computer-simulated CB data and demonstrate that our algorithm yields results where spatial resolution and image noise are distributed much more uniformly over the field-of-view, compared to Feldkamp＇s approach.
文摘Based on the geometrical relationships between image pixels and projection rays at different viewing angles,a Multiorientation Simultaneous Back Projection (MSBP) approach is proposed in this papar for two-dimensional (2-D) parallel and fan beam CT systems. In this scheme, backprojections for eight views, 6, π/2 - θ, π/2 + 6, π- θ, π+ θ, 3π/2 - θ, 3π/2 + θ, and 2π- θ, are implemented at the same time,while the locating operation of pixels for interpolation and computation of weighting parameters are only required for one of them when one half of the number of thaws is even. Implementation remits on an Intel 80386 hosed computer show that the proposed method has a notable computational gain,compared with the conventional implementation of backprojection.
