Statistical iterative reconstruction (IR) techniques have demonstrated many advantages in X-ray CT reconstruction. The statistical iterative reconstruction approach is often modeled as an optimization problem including a data fitting function and a penalty function. The tuning parameter values that regulate the strength of the penalty function are critical for achieving good reconstruction results. However, appropriate tuning parameter values that are suitable for the scan protocols and imaging tasks are often difficult to choose. In this work, we propose a path seeking algorithm that is capable of generating a series of IR images with different strengths of the penalty function. The path seeking algorithm uses the ratio of the gradients of the data fitting function and the penalty function to select pixels for small fixed size updates. We describe the path seeking algorithm for penalized weighted least squares (PWLS) with a Huber penalty function in both the directions of increasing and decreasing tuning parameter value. Simulations using the XCAT phantom show the proposed method produces path images that are very similar to the IR images that are computed via direct optimization. The root-mean- squared-error of one path image generated by the proposed method relative to full iterative reconstruction is about 6 HU for the entire image and 10 HU for a small region. Different path seeking directions, increment sizes and updating percentages of the path seeking algorithm are compared in simulations. The proposed method may reduce the dependence on selection of good tuning parameter values by instead generating multiple IR images, without significantly increasing the computational load.
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.
In computed tomography (CT), the nonlinear characteristics of beam hardening are due to the polychromaticity of X-rays, which severely degrade the CT image quality and diagnostic accuracy. The correction of beam hardening has been an active area since the early years of CT, and various techniques have been developed. State of-the-art works on multi-material beam hardening correction (BHC) are mainly based on segmenting datasets into different materials, and correcting the non-linearity iteratively. Those techniques are limited in correction effectiveness due to inaccurate segmentation. Furthermore, most of them are computationally intensive. In this study, we introduce a fast BHC scheme based on frequency splitting with the fact that beam hardening artifacts mainly contain in the low frequency components and take more iterations to be corrected in comparison with high frequency components. After low-pass filtering and correcting artifacts at down-sampled projections, an artifact reduced high resolution reconstruction will be obtained by incorporating the original edge information from the high frequency components. Evaluations in terms of correction accuracy and computational efficiency are performed using simulated and real CT datasets. In comparison to the BHC algorithm without frequency splitting, the proposed accelerated algorithm yields comparable results in correcting cupping and streak artifacts with tremendously reduced computational effort. We conclude that the presented framework can achieve a significant speedup while still obtaining excellent artifact reduction. This is a significant practical advantage for clinical as well as industrial CT.