## 1 Introduction
[21] used partial voxel interpolation to reduce errors in cardiac CT ventricular volume measurements. [PERSON] et al. [22] estimated the length of partial cracks in epoxy materials based on the ratio of grayscale values between pixels containing partial cracks to those of pure epoxy materials. [PERSON] et al. [23] integrated decision tree classification algorithms and particle histogram parameters to achieve the quantitative assessment of mineral compositions inside particles, considering the inter-phase partial volume effect. Some researchers have combined imaging techniques of different resolutions, such as nano-CT with micro-CT or electron tomography [24; 25; 26; 27], to obtain multi-scale structural information of samples. In many fields, it is often necessary to establish the three-dimensional digital structure of materials for numerical simulations of their physical and chemical properties. While X-ray CT allows non-destructive imaging of sample three-dimensional structures, the trade-off between imaging field of view and resolution remains challenging. High imaging resolution enables capturing detailed structural features of the samples, but limits the imaging field of view, restricting the statistical representativeness of numerical simulation results. For instance, in unconventional energy reservoir structure characterization, natural rock samples contain pores of different scales. Due to the influence of the partial volume effect and other factors, pore structure information will be lost when extracting rock pores, resulting in the deviation of permeability calculation. Establishing a three-dimensional physical field of the samples based on high-resolution results can lead to impractical data volumes. [PERSON] et al. used deep learning to enhance low-resolution images on a large-sample scale, creating multi-scale models capable of accurately simulating fluid dynamics experiments from pore (micrometer) to continuum (centimeter) scales [28]. [PERSON] et al. [29] proposed a flexible ternary segmentation method to accurately express the contribution of partial pores to rock permeability. Despite advancements in methods to mitigate the partial volume effect on CT image analysis and physical modelling, accurately obtaining quantitative information on partially occupied CT voxel compositions to characterize material multi-scale structures remains challenging. [PERSON] et al. [30] proposed data-constrained modelling, which assumed that the theoretical X-ray linear attenuation coefficient of each voxel is the volume-weighted average of the X-ray linear attenuation coefficients of all compositions contained within it. By minimizing the difference between theoretical and reconstructed X-ray linear attenuation coefficients and maximizing the Boltzmann statistical distribution probability of the materials of all voxels, the volume fractions of different compositions within each voxel can be calculated. This method has been successfully applied in synchrotron X-ray CT data analysis. The excellent monochromaticity of synchrotron X-rays greatly facilitates determining the theoretical X-ray linear attenuation coefficients of sample CT voxels. Combining this method with synchrotron CT has achieved successful applications in some fields [31; 32; 33]. Despite achieving a certain degree of success in synchrotron CT image analysis, the practical application of DCM is limited due to the high cost of the beamline time of synchrotron CT. Laboratory micro-CT is more common, but it uses an X-ray tube as the light source, producing continuous spectrum (polychromatic) X-rays. Compared to the quasi-monochromatic X-rays used in synchrotron CT, the continuous spectrum X-rays pose challenges in establishing the correlation between material elemental compositions and CT slice X-ray linear attenuation coefficients, which is energy-dependent. This study is a quantitative investigation of six artificial samples with known overall compositions and volume fractions.