Physics-based spectral compensation algorithm for x-ray CT with primary modulator

Abstract

X-ray computed tomography (CT) scatter correction using primary modulator has been continuously developed over the past years, with progress in improving the performance of scatter correction. In this work, we further advance the primary modulator technique towards practical applications where the spectral nonuniformity caused by the modulator continues to be a challenging problem. A physics-based spectral compensation algorithm is proposed to adaptively correct for the spectral nonuniformity, and hence to reduce the resultant ring artifacts on reconstructed CT images. First, an initial spectrum of the CT system without the primary modulator is modeled using an understanding of x-ray CT physics, and optimized by an expectation maximization method; then, the optimized estimation of the initial spectrum is utilized to adaptively calculate the effective modulator thickness from measured transmissions of the primary modulator at each detector element, leading to a set of new spectra that is able to capture the nonuniform spectral distribution of the primary modulator; finally, using the modulator-modeled spectrum, a beam hardening mapping function is generated and beam hardening correction is applied to CT projections. A CatPhan600 phantom and an anthropomorphic thorax phantom were scanned with three different primary modulators to evaluate the approach. For the Catphan phantom, the spectral compensation algorithm efficiently removes the ring (and band) artifacts that otherwise dominate the reconstructed CT image. For the three modulators with nominal copper thickness of 52.5, 105 and 210 m, our method reduces the CT number nonuniformity from 147.9, 436.2 and 696.4 Hounsfield units (HU) to 14.6, 26.2 and 13.6 HU, respectively, close to that of the reference image (i.e. 7.5 HU). For the thorax phantom, the ring artifacts are also suppressed significantly on the transaxial image; on the sagittal image, the alternating black-and-white patterns are largely removed, with the CT number nonuniformity being reduced from 282.0 HU to 38.5 HU.

Empirical beam hardening and ring artifact correction for x‐ray grating interferometry (EBHC‐GI)

“…Polynomial corrections are an empirical prereconstruction beam hardening correction technique for conventional (absorption) x‐ray imaging of objects dominated by a single material 15 that map polychromatic projections to monochromatic projections . Empirical cupping correction (ECC) 17 is one such polynomial correction that assumes this mapping to be of the form:for an degree polynomial.…”

“…Additionally, gratings with translucent lamellae, a possible result of manufacturing errors, 14 have been shown to further harden the beam 9 . Given that grating transmission can vary over its area this can result in spectral nonuniformities as photons passing through different regions experience varying degrees of hardening 15 . Thus a suitable correction scheme for grating interferometry must account for both the beam hardening from the sample as well as the spectral artifacts from the gratings.…”

“…Analytical methods overcome the need for phantom calibration scans but require detailed system knowledge of the source spectra and detector response, while making assumptions on spectral responses of the sample and gratings 10 . One solution developed to compensate for spectral artifacts from primary modulators lessens these assumptions by using iterative methods to estimate both the spectra and the effective modulator thickness at each detector pixel 15 . Applied to grating interferometry such an approach would have to be expanded to estimate the effective thicknesses and spectral responses of all three gratings.…”

Densely sampled spectral modulation for x‐ray CT using a stationary modulator with flying focal spot: a conceptual and feasibility study of scatter and spectral correction

“…Once the estimated scatter is removed from the measured CT data, spectral compensation for the modulator can be implemented to remove the spectral nonuniformity. 30 Here, the above scatter estimation algorithm is denoted SE sps , which includes both scatter correction and spectral compensation for modulator. The overall process of SE sps algorithm for CT using DSSM with SMFFS is illustrated in Fig.…”

“…Regarding problem (1), recently a physics‐based spectral compensation scheme has been developed for x‐ray CT with a modulator 30 . The estimated system spectra with no modulator in the beam [] were obtained using the expectation maximization (EM) method, 31 which mainly consists of two steps: (1) collecting the transmission data for a variety of known materials and thicknesses (in our case, 0.5 ∼ 12.75 mm for Al; and 0.33 and 2.1 mm for Cu); and (2) tuning the system spectrum using the EM algorithm to reduce the overall error between the simulated transmission data and their corresponding measured ones.…”