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8 March 2012 On the numerical implementation of discrete finite Hilbert transform for image reconstruction
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The finite Hilbert transform plays an essential role in the recently developed derivative back projection (DBP) image reconstruction methods. The accuracy of the numerical methods in implementing the finite Hilbert transform has a significant impact on the reconstruction algorithms' performance. A number of numerical implementations using linear and sinc interpolation kernels have been developed to carry out the Hilbert transform. In this study, we propose a new numerical method using a non-linear interpolation kernel to implement the finite Hilber transform. We evaluate the performance of the proposed non-linear implementation of the finite Hilbert transform in DBP image reconstruction and compare it with that of the implementations using the linear and sinc interpolation kernels, in which the contrast-to-noise ratio, noise power spectrum and modulation transfer function are investigated. The preliminary results show that the finite Hilbert transform implemented with the nonlinear interpolation kernel exhibits slightly better noise performance than the ones implemented with the linear or sinc interpolation.
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Yi Yang, Shaojie Tang, and Xiangyang Tang "On the numerical implementation of discrete finite Hilbert transform for image reconstruction", Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 831336 (8 March 2012);

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