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In this paper, we present a multichannel cross-modal fusion algorithm to combine two complementary modalities in electron tomography: X-ray spectroscopy and scanning transmission electron microscopy (STEM). The former reveals compositions with high elemental specificity but low signal-to-noise ratio (SNR), while the latter characterizes the structure with high SNR but little chemical information. We use a multivariate regression to build a cross-modal fusion framework for these two modalities to simultaneously achieve high elemental specificity and high SNR for a target element chosen from the sample under study. Specifically, we first compute three-dimensional tomograms from tilt-series datasets of X-ray and STEM using different reconstruction algorithms. Then, we generate many feature images from each tomogram. Finally, we adopt partial least squares regression to assess the connection between these feature images and the reconstruction of the target element. Based on the simulated and experimental datasets of semiconductor devices, we demonstrate that our algorithm can not only produce continuous edges, homogeneous foreground, and clean background in its element-specific reconstructions but also can more accurately preserve fine structures than state-of-the-art tomography techniques. Moreover, we show that it can deliver results with high fidelity even for X-ray datasets with limited tilts or low counts. This property is highly desired in the semiconductor industry where acquisition time and sample damage are essential.