Inverse problems arise when we want to use data to extract an insight into the inner workings of a system. Such problems are often ill-posed, meaning that there are multiple explanations compatible with the observations and it is therefore necessary to constrain the problem to arrive at a concrete solution. High-throughput high-resolution genome-wide spatial transcriptomics data is a recent breakthrough technology presenting great promise for gaining insights into cellular interactions and tissue-level systems biology. Extracting biologically useful knowledge from this new data modality comes with a novel set of computational challenges. One such challenge is figuring out how much different cell types have contributed to each spatial point measured from the tissue. We will go step-by-step over a simple, intuitive and interpretable solution (manifested by a matrix factorization) that utilizes expert-annotated reference data of cell types to constrain this ill-posed inverse problem.