Scatter correction based on quasi-Monte Carlo for CT reconstruction

Abstract

Scatter signals can degrade the contrast and resolution of computed tomography (CT) images and induce artifacts. How to effectively correct scatter signals in CT has always been a focal point of research for researchers. This work presents a new framework for eliminating scatter artifacts in CT. In the framework, the interaction between photons and matter is characterized as a Markov process, and the calculation of the scatter signal intensity in CT is transformed into the computation of a $4n$-dimensional integral, where $n$ is the highest scatter order. Given the low-frequency characteristics of scatter signals in CT, this paper uses the quasi-Monte Carlo (QMC) method combined with forced fixed detection and down sampling to compute the integral. In the reconstruction process, the impact of scatter signals on the X-ray energy spectrum is considered. A scatter-corrected spectrum estimation method is proposed and applied to estimate the X-ray energy spectrum. Based on the Feldkamp-Davis-Kress (FDK) algorithm, a multi-module coupled reconstruction method, referred to as FDK-QMC-BM4D, has been developed to simultaneously eliminate scatter artifacts, beam hardening artifacts, and noise in CT imaging. Finally, the effectiveness of the FDK-QMC-BM4D method is validated in the Shepp-Logan phantom and head. Compared to the widely recognized Monte Carlo method, which is the most accurate method by now for estimating and correcting scatter signals in CT, the FDK-QMC-BM4D method improves the running speed by approximately $102$ times while ensuring accuracy. By integrating the mechanism of FDK-QMC-BM4D, this study offers a novel approach to addressing artifacts in clinical CT.

Figures (9)

• Figure 1: The overall workflow of the proposed reconstruction method FDK-QMC-BM4D, which uses the head as a carrier.
• Figure 2: A simple geometric illustration of photon-matter interaction in CT.
• Figure 3: An illustration of key steps in scatter simulation algorithm.
• Figure 4: Experimental results of the detected energy spectrum estimation for simulated data. (a) is the geometric illustration of the Al phantom; (b) shows the reference spectrum (blue line), the spectrum estimated by EM (green line) after 128 iterations, and the spectrum estimated by EM-SC (red line) after 128 iterations; (c) shows the RMSE of the spectra estimated by EM and EM-SC compared to the reference spectrum, with $N$ representing the number of iterations.
• Figure 5: The polychromatic projection curve of simulated data. (a) and (b) are the polychromatic projection curve of the detected energy spectrum estimated by EM and EM-SC, respectively.