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Iterative algorithms have become increasingly popular in Computed Tomography (CT) image reconstruction since they better deal with the adverse image artifacts arising from low radiation dose image acquisition. But iterative methods remain computationally expensive. The main cost emerges in the projection and backprojection operations where accurate CT system modeling can greatly improve the quality of the reconstructed image. We present a framework that improves upon one particular aspect - the accurate projection of the image basis functions. It differs from current methods in that it substitutes the high computational complexity associated with accurate voxel projection by a small number of memory operations. Coefficients are computed in advance and stored in look-up tables parameterized by the CT system's projection geometry. The look-up tables only require a few kilobytes of storage and can be efficiently accelerated on the GPU. We demonstrate our framework with both numerical and clinical experiments and compare its performance with the current state of the art scheme - the separable footprint method.
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Exact gram filtering and efficient backprojection for iterative CT reconstruction
Abstract PurposeForward and backprojections are the basis of all model‐based iterative reconstruction (MBIR) methods. However, computing these accurately is time‐consuming. In this paper, we present a method for MBIR in parallel X‐ray beam geometry that utilizes a Gram filter to efficiently implement forward and backprojection. MethodsWe propose using voxel‐basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of backprojection. In the special case of parallel X‐ray beam geometry, the forward and backprojection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel‐basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of backprojection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios. ResultsThe proposed method is tested on both phantom and real computed tomography (CT) images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state‐of‐the‐art projection models in terms of speed and accuracy for both backprojection and reconstruction. ConclusionsWe proposed a iterative reconstruction methodology for 3D parallel‐beam X‐ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state‐of‐the‐art projection models on both backprojection and reconstruction results significantly.
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- PAR ID:
- 10388220
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Medical Physics
- Volume:
- 49
- Issue:
- 5
- ISSN:
- 0094-2405
- Page Range / eLocation ID:
- p. 3080-3092
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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