Mass spectrometry imaging (MSI) has been a key driver of groundbreaking discoveries in a number of fields since its inception more than 50 years ago. Recently, MSI development trends have shifted towards ambient MSI (AMSI) as the removal of sample-preparation steps and the possibility of analysing biological specimens in their natural state have drawn the attention of multiple groups across the world. Nevertheless, the lack of spatial resolution has been cited as one of the main limitations of AMSI. While significant research effort has presented hardware solutions for improving the resolution, software solutions are often overlooked, although they can usually be applied in a cost-effective manner after image acquisition. In this vein, we present two computational methods that we have developed to directly enhance the image resolution post-acquisition. Robust and quantitative resolution improvement is demonstrated for 12 cases of openly accessible datasets across laboratories around the globe. Using the same universally applicable Fourier imaging model, we discuss the possibility of true super-resolution by software for future studies.