Empirical cupping correction: A first‐order raw data precorrection for cone‐beam computed tomography

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Abstract
We propose an empirical cupping correction (ECC) algorithm to correct for CT cupping artifacts that are induced by nonlinearities in the projection data. The method is raw data based, empirical, and requires neither knowledge of the x-ray spectrum nor of the attenuation coefficients. It aims at linearizing the attenuation data using a precorrection function of polynomial form. The coefficients of the polynomial are determined once using a calibration scan of a homogeneous phantom. Computing the coefficients is done in image domain by fitting a series of basis images to a template image. The template image is obtained directly from the uncorrected phantom image and no assumptions on the phantom size or of its positioning are made. Raw data are precorrected by passing them through the once-determined polynomial. As an example we demonstrate how ECC can be used to perform water precorrection for an in vivo micro-CT scanner (TomoScope 30 s, VAMP GmbH, Erlangen, Germany). For this particular case, practical considerations regarding the definition of the template image are given. ECC strives to remove the cupping artifacts and to obtain well-calibrated CT values. Although ECC is a first-order correction and cannot compete with iterative higher-order beam hardening or scatter correction algorithms, our in vivo mouse images show a significant reduction of bone-induced artifacts as well. A combination of ECC with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.