Fig. 1: Schema of SpaGFT for spatial omics representation.

a The panel showcases spatial omics technologies, including single and multi-modality methods. b–d the panels display the calculation of Fourier modes (FM), and the transformation of original graph signals into Fourier coefficients (FC) with different resolutions of technologies. b The figure presents pixel graphs with nodes at the subcellular level and edges denoting short Euclidean distances between connected pixels. This graph represents technologies like stere-seq and most spatial proteomics data, e.g., 4i. The two figures following panel b illustrate a k-bandlimited signal (e.g., Afp) and a non-k-bandlimited signal (e.g., Xbp1). c and d Cell graphs and spot graphs are composed of nodes at the cellular level resolution and multicellular level resolution, respectively, with edges representing short Euclidean distances between nodes in two panels. e The figure exhibits multi-modal data from a technology called SPOTS, which can measure both proteins and genes simultaneously. The k-bandlimited signal shown is for the Ly6a gene and its corresponding protein, while the non-k-bandlimited signal is for the Klrb1c gene. f–h The panels show examples of signals from Slide-DNA-seq, Slide-TCR-seq, and spatial epigenome–transcriptome co-profiling of mouse embryo-13. i The panel shows subcellular spatial proteome (i.e., 4i) are k-bandlimited signals. j This panel demonstrates data augmentation for sequencing-based spatial transcriptomics (e.g., Visium). The first step of augmentation involves using H&E images and Cellpose for cell segmentation and counting the number of nuclei in each spot. The next step involves mapping reads to the microbiome genome, which then allows for the determination of microbiome abundance. Finally, gene lists (e.g., MSigDB) can be used to calculate the pathway activity score for each spot. k This panel displays the signals mentioned in panel j, including cell density, microbiome abundance, and pathway activity. Panel a is created with BioRender.com, created with BioRender.com, released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license.