A scattering correction method for CT reconstruction based on the Wavelet Adaptive Material-dependent Boltzmann Transport Equation (WAM-BTE)

Abstract

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.