Empirical cupping correction for CT scanners with primary modulation (ECCP)

X-ray CT measures the attenuation of polychromatic x-rays through an object. The rawdata acquired, which are the negative logarithm of the relative x-ray intensity behind the patient, must undergo water precorrection to linearize the measurement and to convert them into line integrals that are ready for reconstruction. The function to linearize the measured projection data depends on the detected spectrum of the ray. This spectrum may vary as a function of the detector position, e.g. in cases where the heel effect becomes relevant, or where a bow-tie filter introduces channel-dependent beam hardening, or in cases where a primary modulator is used to modulate the primary intensity of the spectrum. We propose a new approach that allows to handle these effects. Our empirical cupping correction for primary modulation (ECCP) corrects for artifacts, such as cupping artifacts or ring artifacts, that are induced by non-linearities in the projection data due to spatially varying pre- or post filtration of the x-rays. To do so, ECCP requires nothing but a simple scan of a homogeneous phantom of nearly arbitrary shape. Based on this information, coefficients of a polynomial series are calculated and stored for later use. Numerical examples and physical measurements are shown to demonstrate the quality of the precorrection. ECCP achieves to remove the cupping artifacts and to obtain well-calibrated CT-values even in cases of strong primary modulation. A combination of ECCP with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.