AI 中文总结
本研究针对CT成像中散射光子导致图像质量下降的问题，提出基于WAM-BTE的散射校正方法，结合小波分解构建自适应多尺度框架，在保证精度的同时大幅提升计算效率，单视图散射计算达毫秒级。
AI 中文摘要
X射线计算机断层扫描（CT）是临床诊断中必不可少的成像技术。然而，散射光子会降低图像对比度并引入CT值偏差，严重降低图像质量。近年来，基于玻尔兹曼输运方程（BTE）的散射校正方法因具有高物理精度和灵活性而受到越来越多的关注。不过，现有的基于BTE的方法通常采用单材料模型，无法准确描述不同材料中光子相互作用截面的非线性能量依赖性。本研究提出了一种基于小波自适应材料相关BTE（WAM-BTE）的散射校正方法，通过引入材料相关的散射分布，将传统单材料模型扩展为多材料模型；此外，通过小波分解构建了自适应多尺度框架，利用低频小波系数进行粗尺度散射估计以降低计算复杂度，同时利用高衰减材料的高频小波能量进行自适应局部细化。理论分析表明，当使用Haar基函数时，第w级的低频小波系数在数学上等价于尺度因子为2^w的块平均下采样，仅存在一个确定的归一化因子。实验结果显示，所提出的WAM-BTE方法达到了与蒙特卡罗方法相当的精度，同时保留了粗尺度估计的计算效率，单个投影视图的散射计算时间缩短至毫秒级。
英文摘要
X-ray computed tomography (CT) is an essential imaging technology in clinical diagnosis. However, scattered photons can reduce image contrast and introduce CT value bias, which severely degrades image quality. Recently, scatter correction methods based on the Boltzmann transport equation (BTE) have attracted increasing attention due to their high physical accuracy and flexibility. Nevertheless, existing BTE-based methods usually employ single-material models, which cannot accurately describe the nonlinear energy dependence of photon interaction cross-sections in different materials. In this work, a scatter correction method based on the wavelet adaptive material-dependent BTE (WAM-BTE) is proposed. The conventional single-material model is extended to a multi-material model by introducing material-dependent scattering distributions. Furthermore, an adaptive multi-scale framework is established through wavelet decomposition. The low-frequency wavelet coefficients are used for coarse-scale scatter estimation to reduce computational complexity, while the high-frequency wavelet energy of high attenuation materials is utilized for adaptive local refinement. Theoretical analysis demonstrates that, when using the Haar basis function, the low-frequency wavelet coefficients at the $w$-th level are mathematically equivalent to block-average downsampling with a scale factor of $2^w$, except for a deterministic normalization factor. Experimental results show that the proposed WAM-BTE method achieves comparable accuracy to the Monte Carlo method while preserving the computational efficiency of coarse-scale estimation. The scatter calculation time for a single projection view is reduced to the millisecond level.
