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AbstractComputed Tomography CT scanners evolved from simple parallel-beam geometry into more complex fan-beam geometry Fan-beam reconstruction algorithms were derived from parallel-beam geometry The associated filtered-backprojection FBP algorithm requires a computationally expensive pixel-dependent weight factor in the backprojector The rebinning mechanism to convert fan-beam projections to parallel-beam projections is one of the methods simplifying the reconstruction of the CT image A common approach to perform fan-beam to parallel-beam rebinning is a two-step process using interpolation methods In the first step azimuthal interpolation is carried out only across projection views to arrive at a set of non-uniformly spaced parallel samples The uniformly spaced parallel-beam projections are obtained by second radial interpolation Different interpolation methods lead to different numerical presentations and noisy textures in the reconstructed images This paper evaluates three interpolation methods linear frequency domain and higher order in rebinning fan-beam data into parallel-beam data in the framework of the FBP algorithm in parallel-beam CTs The high-contrast spatial resolution modulation transfer function MTF and noise are used to quantify the image quality The MTF is obtained by calculating the magnitude of the Fourier transform of point spread function PSF using a thin object The noise is expressed as the noise power spectrum NPS and noise variance of the reconstructed image containing only Poisson distributed noise Our results show that the higher order interpolation cubic-spline is the most helpful to improve the image quality in rebinning We further demonstrate that the rebinning data gives more satisfactory results for assessment of MTF NPS and noise variance in comparison with the fan-beam dataKeywords computed tomography rebinning image reconstruction modulation transfer fuction MTF noise power spectrum NPSI IntroductionIn CT the key to image reconstruction is Fourier slice theorem which relates the measured projection data to the two-dimensional Fourier transform of the object cross section Kak It is derived by taking the one-dimensional Fourier transform of a parallel projection and noting that it is equal to a slice of the two-dimensional Fourier
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