SPROUT: spectral sparsification helps restore the spatial structure at single-cell resolution.

Single-cell RNA sequencing thoroughly quantifies the individual cell transcriptomes but renounces the spatial structure. Conversely, recently emerged spatial transcriptomics technologies capture the cellular spatial structure but skimp cell or gene resolutions. Ligand-receptor interactions reveal the potential of cell proximity since they are spatially constrained. Cell-cell affinity values estimated by ligand-receptor interaction can partially represent the structure of cells but falsely include the pseudo affinities between distant or indirectly interacting cells. Here, we develop a software package, SPROUT, to reconstruct the single-cell resolution spatial structure from the transcriptomics data through diminished pseudo ligand-receptor affinities. For spatial data, SPROUT first curates the representative single-cell profiles for each spatial spot from a candidate library, then reduces the pseudo affinities in the intercellular affinity matrix by partial correlation, spectral graph sparsification, and spatial coordinates refinement. SPROUT embeds the estimated interactions into a low-dimensional space with the cross-entropy objective to restore the intercellular structures, which facilitates the discovery of dominant ligand-receptor pairs between neighboring cells at single-cell resolution. SPROUT reconstructed structures achieved shape Pearson correlations ranging from 0.91 to 0.97 on the mouse hippocampus and human organ tumor microenvironment datasets. Furthermore, SPROUT can solely