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The texture based approach is relatively easy too implement and a considerable speed-up is achieved across all platforms. The nearest-neighbor interpolation performs significantly faster if the ALU-based algorithm is used. On some platforms the linear interpolation can be also further accelerated if ALU variant is used alone or in combination with texture-based algorithm. If exact agreement with the standard algorithm is not required, it is possible to enable additional speed-up using the half-float data representation or by replacing the linear interpolation with a combination of oversampling and the nearest-neighbor interpolation. On the newest NVIDIA Titan X GPU, we are able to secure speed-up of 2.5 times using the linear interpolation and without the loose of quality. The proposed algorithm is 3.5 times faster if nearest-neighbor interpolation is required. Even if the reconstruction chain is only able to execute the back-projection kernel with a single-slice at a time, the proposed hybrid approach is 2 times faster when the standard algorithm. The achieved speed-up across other platforms are presented in \figurename~\ref{fig:speedup}.
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\includegraphics[width=0.45\textwidth]{img/speedup.pdf}
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\caption{\label{fig:speedup} The figure evaluates the performance of the proposed algorithms in the precise and approximate modes. The improvements enabled by the optimized texture-based approach are shown in the first bar of each architecture. The second and third bars show the maximum speed-up measured with the fastest available method which is executed using the linear or nearest-neighbor interpolation modes correspondingly. The green lines show the speed-up achieved without any compromise on the quality of reconstruction. The red lines show additional performance gain if half-float data representation is used and/or the oversampling approach is used instead of linear interpolation. }