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首页> 外文期刊>Journal of visual communication & image representation >Computationally efficient filtered-backprojection algorithm for tomographic image reconstruction using Walsh transform
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Computationally efficient filtered-backprojection algorithm for tomographic image reconstruction using Walsh transform

机译：计算效率高的滤波反投影算法，用于使用Walsh变换的断层图像重建

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摘要

In this paper, we discuss the implementation of the filtered-backprojection (FBP) algorithm for tomographic image reconstruction using Walsh transform to exploit its fast computational ability. Walsh transform is the fastest unitary transform known so far. The major advantage of Walsh transform is that it involves only real additions and subtractions whereas Fourier transform involves complex multiplications and additions. Implementation of the proposed algorithm necessitates the design of an appropriate filter in Walsh domain. In this research, the known Fourier filter coefficients have been transformed into Walsh domain, thereby the 1 x N Fourier filter coefficients were converted into an N x N sparse matrix with nonzero elements in a special pattern. The proposed algorithm has been implemented by taken into account of the special nature of the Walsh domain filter coefficients and tested for its performance using the well-known 'Shepp-Logan head phantom' test image. The results demonstrate that the reconstruction strategy has comparable performance with a significant reduction of computing time. For example, with a 128 x 128-pixel image and 180 views, the speedup achieved is fourfold, with reconstructions qualitatively and visually the same as that of FBP algorithm in the Fourier domain.
机译：在本文中，我们讨论了使用Walsh变换来利用层析成像重建的滤波反投影（FBP）算法的实现，以利用其快速的计算能力。沃尔什变换是迄今为止已知的最快的unit变换。 Walsh变换的主要优点是它仅涉及实数加法和减法，而Fourier变换涉及复杂的乘法和加法。所提出算法的实现需要在沃尔什域中设计适当的滤波器。在这项研究中，已知的傅立叶滤波器系数已转换为沃尔什域，从而将1 x N的傅立叶滤波器系数转换为具有非零元素的N x N稀疏矩阵，并且具有特殊的模式。考虑到沃尔什域滤波器系数的特殊性来实施所提出的算法，并使用著名的“谢普·洛根头部幻像”测试图像对其性能进行了测试。结果表明，该重建策略具有可比的性能，并且显着减少了计算时间。例如，对于128 x 128像素的图像和180个视图，所实现的速度提高了四倍，在质量和视觉上都与傅立叶域中的FBP算法相同。

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