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Hyperfast parallel-beam and cone-beam backprojection using the cell general purpose hardware
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Image of FIG. 1.
FIG. 1.

Block diagram of the cell with pictures of one CBE and of the Mercury dual cell-based blade.

Image of FIG. 2.
FIG. 2.

Data reorganization (rebinning) is used to (a) align the projection matrix with one axis of the volume ( axis) and with the direction of convolution and (b) to upsample the detector pixels until they are small enough to be suitable for nearest neighbor interpolation.

Image of FIG. 3.
FIG. 3.

Only small subvolumes fit into the worker. The corresponding raw data patches are DMAed to the worker prior to real-to-ideal rebinning and backprojection.

Image of FIG. 4.
FIG. 4.

A simulated noise-free phantom consisting of fat, water, tissue and bone (contrasts of , 0, 50, and 1000 HU) was reconstructed using the direct and hybrid approach. Note the narrow window width of the subtraction image: the differences between the direct and the hybrid method are below the typical noise level of a CT image and hence negligible.

Image of FIG. 5.
FIG. 5.

In vivo study of a mouse scanned with the TomoScope cone-beam micro-CT scanner (VAMP GmbH, Erlangen, Germany). The Feldkamp reconstruction is cell based and uses our hybrid backprojection. ( HU, HU).


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Timing results for the parallel backprojection for one CPU or one CBE, respectively.

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Timing results for the perspective backprojection for one CPU or one CBE, respectively.

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DMA latencies for the parallel backprojection (with linear interpolation) and the direct and hybrid perspective backprojection of a volume. DMA get: raw data flow from manager to worker. DMA put: volume flow from worker to manager. The statistical error for the parallel backprojection is below and thus shown as zero.

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Top: Parallel backprojection performance. Bottom: perspective backprojection performance. All values have been scaled to 512 projections and pixels and to voxels, respectively. All values were further scaled to a single processing unit, i.e., to one CPU, one FPGA, one GPU and to one CBE, respectively, and to in the case of CPU-based algorithms. The type column specifies the interpolation type, NN or LI, and the type of arithmethic used: +number of bits denotes floating point arithmethics while number of bits stands for integer (fixed point) arithmetics.

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Possible alignment steps of the projection data to allow for convolution along and to introduce a number of zeroes in the backprojection matrix. Our hybrid code versions perform the convolution alignment , assume the convolution to be performed elsewhere, and finally use the 3D perspective transform matrix for backprojection.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hyperfast parallel-beam and cone-beam backprojection using the cell general purpose hardware