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. 2022 Sep 20;12:15687. doi: 10.1038/s41598-022-19365-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Comparison of statistical (distribution) and spatial (variograms) properties of variables from real MSI (a) and synthetic spatial data (b). (A) Top row: The variograms (right) of an example single ion (middle) from different regions are shown in its histology image (left). Middle row: the 2D image of a few molecular ions from real MSI data and their density plot in the bottom row. (B) The synthetic spatial data image (left), density plot (middle), and the variograms (right) from synthetic data. The variograms (left column) and density plots (middle column) from synthetic data.