A practical statistical polychromatic image reconstruction for computed tomography using spectrum binning

Abstract

Polychromatic statistical reconstruction algorithms have very high computational demands due to the difficulty of the optimization problems and the large number of spectrum bins. We want to develop a more practical algorithm that has a simpler optimization problem, a faster numerical solver, and requires only a small amount of prior knowledge. In this paper, a modified optimization problem for polychromatic statistical reconstruction algorithms is proposed. The modified optimization problem utilizes the idea of determining scanned materials based on a first pass FBP reconstruction to fix the ratios between photoelectric and Compton scattering components of all image pixels. The reconstruction of a density image is easy to solve by a separable quadratic surrogate algorithm that is also applicable to the multi-material case. In addition, a spectrum binning method is introduced so that the full spectrum information is not required. The energy bins sizes and attenuations are optimized based on the true spectrum and object. With these approximations, the expected line integral values using only a few energy bins are very closed to the true polychromatic values. Thus both the problem size and computational demand caused by the large number of energy bins that are typically used to model a full spectrum are reduced. Simulation showed that three energy bins using the generalized spectrum binning method could provide an accurate approximation of the polychromatic X-ray signals. The average absolute error of the logarithmic detector signal is less than 0.003 for a 120 kVp spectrum. The proposed modified optimization problem and spectrum binning approach can effectively suppress beam hardening artifacts while providing low noise images.

Multi-material blind beam hardening correction in near real-time based on non-linearity adjustment of projections

“…Statistical correction methods [24][25][26][27][28][29][30]33] exploit multiple information to correct the BH artifacts in the X-ray images. Such information includes the polychromatic nature of the source, the detector model, the noise distribution, the measurement non-linearity, and the scatter effect are all used in the statistical methods in which they are all incorporated into the maximum likelihood (ML) algorithm [2].…”

Multi-materials beam hardening artifacts correction for computed tomography (CT) based on X-ray spectrum estimation

“…Dual-energy method can provide CT images at different monochromatic photon energies from dual kVp scans and these images are beam hardening artifacts free in principle [7], [11], [12], [13], [14], [15], but due to the extra calibration measurement and CNR reduction at some energy level, dual-energy can only be applied in some specific applications right now [15]. BHC methods based on iterative reconstruction try to incorporate the polychromatic attenuation nature into the update procedure to reconstruct beam hardening artifacts free images [8], [9], [10], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Instead of using a simple monochromatic projection acquisition model, [9] employed a polychromatic acquisition model and decomposed the energy-dependent linear attenuation coefficient into a photonelectric component and a Compton scatter component.…”