Chemical imaging techniques are increasingly being used in combination to achieve a greater understanding of a sample. This is especially true in the case of mass spectrometry imaging (MSI), where the use of different ionization sources allows detection of different classes of molecules across a range of spatial resolutions. There has been significant recent effort in the development of data fusion algorithms that attempt to combine the benefits of multiple techniques, such that the output provides additional information that would have not been present or obvious from the individual techniques alone. However, the majority of the data fusion methods currently in use rely on image registration to generate the fused data and therefore can suffer from artifacts caused by interpolation. Here, we present a method for data fusion that does not incorporate interpolation-based artifacts into the final fused data, applied to data acquired from multiple chemical imaging modalities. The method is evaluated using simulated data and a model polymer blend sample, before being applied to biological samples of mouse brain and lung.