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Backprojection
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Gengsheng L. Zeng – One of the best experts on this subject based on the ideXlab platform.

Listmode data reconstruction via the finite Hilbert transform of the derivative of the Backprojection
2007 IEEE Nuclear Science Symposium Conference Record, 2007CoAuthors: Gengsheng L. ZengAbstract:An exact analytical image reconstruction method is presented for twodimensional (2D) imaging. The method performs Backprojection, the derivative and finite Hilbert transforms. This method can be applied to many imaging geometries. The Backprojection procedure is imaging geometry dependent, while the differentiation and the finite Hilbert transform procedures are identical for all imaging geometries. This algorithm is applicable to listmode data in nuclear medicine, while other filtered Backprojection algorithms cannot be applied directly to the listmode data.

Image reconstruction via the finite Hilbert transform of the derivative of the Backprojection.
Medical Physics, 2007CoAuthors: Gengsheng L. ZengAbstract:An exact analytical image reconstruction method is presented for twodimensional imaging. The method performs Backprojection, the derivative and finite Hilbert transforms. This method can be applied to many imaging geometries. The Backprojection procedure is imaginggeometry dependent, while the differentiation and the finite Hilbert transform procedures are identical for all imaging geometries. This algorithm is applicable to listmode data in nuclear medicine, while other filtered Backprojection algorithms cannot be applied directly to the listmode data.

Backprojection filtering for variable orbit fanbeam tomography
IEEE Transactions on Nuclear Science, 1995CoAuthors: Grant T. Gullberg, Gengsheng L. ZengAbstract:Backprojection filtering algorithms are presented for three variable orbit fanbeam geometries. Expressions for the fanbeam projection and Backprojection operators are given for a flat detector fanbeam geometry with fixed focal length, with variable focal length, and with fixed focal length and offcenter focusing. Backprojection operators are derived for each geometry using transformation of coordinates to transform from a parallel geometry backprojector to a fanbeam backprojector for the appropriate geometry. The Backprojection operator includes a factor which is a function of the coordinates of the projection ray and the coordinates of the pixel in the backprojected image. The Backprojection filtering algorithm first backprojects the variable orbit fanbeam projection data using the appropriately derived backprojector to obtain a 1/r blurring of the original image, then takes the twodimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, then multiples the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. Computer simulations verify that backprojectors with appropriate weighting give artifact free reconstructions of simulated line integral projections. Also, it is shown that it is not necessary to assume a projection model of line integrals, but the projector and backprojector can be defined to model the physics of the imaging detection process. A backprojector for variable orbit fanbeam tomography with fixed focal length is derived which includes an additional factor which is a function of the flux density along the flat detector. It is shown that the impulse response for the composite of the projection and Backprojection operations is equal to 1/r. >
Grant T. Gullberg – One of the best experts on this subject based on the ideXlab platform.

Backprojection filtering for variable orbit fanbeam tomography
IEEE Transactions on Nuclear Science, 1995CoAuthors: Grant T. Gullberg, Gengsheng L. ZengAbstract:Backprojection filtering algorithms are presented for three variable orbit fanbeam geometries. Expressions for the fanbeam projection and Backprojection operators are given for a flat detector fanbeam geometry with fixed focal length, with variable focal length, and with fixed focal length and offcenter focusing. Backprojection operators are derived for each geometry using transformation of coordinates to transform from a parallel geometry backprojector to a fanbeam backprojector for the appropriate geometry. The Backprojection operator includes a factor which is a function of the coordinates of the projection ray and the coordinates of the pixel in the backprojected image. The Backprojection filtering algorithm first backprojects the variable orbit fanbeam projection data using the appropriately derived backprojector to obtain a 1/r blurring of the original image, then takes the twodimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, then multiples the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. Computer simulations verify that backprojectors with appropriate weighting give artifact free reconstructions of simulated line integral projections. Also, it is shown that it is not necessary to assume a projection model of line integrals, but the projector and backprojector can be defined to model the physics of the imaging detection process. A backprojector for variable orbit fanbeam tomography with fixed focal length is derived which includes an additional factor which is a function of the flux density along the flat detector. It is shown that the impulse response for the composite of the projection and Backprojection operations is equal to 1/r. >

Backprojection filtering for variable orbit fan beam tomography
Proceedings of 1994 IEEE Nuclear Science Symposium – NSS'94, 1994CoAuthors: Grant T. Gullberg, Gengsheng L. ZengAbstract:A Backprojection filtering algorithm is presented for variable orbit fanbeam tomography. Expressions for the fan beam projection and Backprojection operators are given for a fanbeam geometry with flat detector. The Backprojection operator is derived such that the impulse response for the composite of the projection and Backprojection operations is equal to l/r if the data are acquired over 360 degrees. The algorithm first backprojects the variable orbit fanbeam projection data using the newly derived backprojector, takes the twodimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, multiplies the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. The Backprojection operator includes a factor which is a function of the flux density along the flat detector which is a function of the rate of change of the orbit radius as a function of angle. The algorithm is verified using computer simulations. >

A study of reconstruction artifacts in cone beam tomography using filtered Backprojection and iterative EM algorithms
IEEE Transactions on Nuclear Science, 1990CoAuthors: Gengsheng L. Zeng, Grant T. GullbergAbstract:Reconstruction artifacts in cone beam tomography are studied for filtered Backprojection (Feldkamp) and iterative EM algorithms. The filtered Backprojection algorithm uses a voxeldriven, interpolated Backprojection to reconstruct the cone beam data, whereas the iterative EM algorithm performs raydriven projection and Backprojection operations for each iteration. Two weighting schemes for the projection and Backprojection operations in the EM algorithm are studied. One weights each voxel by the length of the ray through the voxel and the other equates the value of a voxel to the functional value of the midpoint of the line intersecting the voxel, which is obtained by interpolating between eight neighboring voxels. Cone beam reconstruction artifacts such as rings, bright vertical extremities, and slicetoslice crosstalk are not found with parallel beam and fan beam geometries. When using filtered Backprojection and iterative EM algorithms, the linelength weighting is susceptible to ring artifacts which are improved by using interpolated projectorbackprojectors. >
Michel Desvignes – One of the best experts on this subject based on the ideXlab platform.

Algorithm Architecture Adequacy for High Speed 3D Tomography
, 2007CoAuthors: Nicolas Gac, Stéphane Mancini, Michel Desvignes, Dominique HouzetAbstract:Backprojection is a computational costly step in tomography image reconstruction such as Positron Emission Tomography (PET). In this purpose, this paper presents a Pipelined, Prefetch and Parallelized Architecture for PET Backprojection (3PAPET). The main strength of this architecture comes from its original memory access strategy, masking the high memory latency of the external memory. The 3PAPET architecture is implemented on a System on Programmable Chip (SopC). Time performances are compared with a desktop PC, a workstation and a GPU. We prove that the exploitation of the intrinsic temporal and spatial locality by the 3D Predictive and Adaptative (3DAP) memory cache succeeds to run efficiently several pipelines of Backprojection : each reaches a computational throughput close to 1 operation per cycle.

SAC – Hardware/software 2D3D Backprojection on a SoPC platform
Proceedings of the 2006 ACM symposium on Applied computing – SAC '06, 2006CoAuthors: Nicolas Gac, Stéphane Mancini, Michel DesvignesAbstract:The reduction of image reconstruction time is needed to spread the use of PET for research and routine clinical practice. In this purpose, this article presents a hardware/software architecture for the acceleration of 3D Backprojection based upon an efficient 2D Backprojection. This architecture has been designed in order to provide a high level of parallelism thanks to an efficient management of the memory accesses which would have been otherwise strongly slowed by the external memory. The reconstruction system is embedded in a SoPC platform (System on Programmable Chip), the new generation of reconfigurable circuit. The originality of this architecture comes from the design of a 2D Adaptative and Predictive Cache (2DAP Cache) which has proved to be an efficient way to overcome the memory access bottleneck. Thanks to a hierarchical use of this cache, several Backprojection operators can run in parallel, accelerating in this manner noteworthy the reconstruction process. This 2D reconstruction system will next be used to speed up 3D image reconstruction.

Hardware/software 2D3D Backprojection on a SoPC platform
, 2006CoAuthors: Nicolas Gac, Stéphane Mancini, Michel DesvignesAbstract:The reduction of image reconstruction time is needed to spread the use of PET for research and routine clinical practice. In this purpose, this article presents a hardware/software architecture for the acceleration of 3D Backprojection based upon an efficient 2D Backprojection. This architecture has been designed in order to provide a high level of parallelism thanks to an efficient management of the memory accesses which would have been otherwise strongly slowed by the external memory. The reconstruction system is embedded in a SoPC platform (System on Programmable Chip), the new generation of reconfigurable circuit. The originality of this architecture comes from the design of a 2D Adaptative and Predictive Cache (2DAP Cache) which has proved to be an efficient way to overcome the memory access bottleneck. Thanks to a hierarchical use of this cache, several Backprojection operators can run in parallel, accelerating in this manner noteworthy the reconstruction process. This 2D reconstruction system will next be used to speed up 3D image reconstruction.