  Spatially resolved transcriptomics (ST) measures gene expression along with
the spatial coordinates of the measurements. The analysis of ST data involves
significant computation complexity. In this work, we propose gene expression
dimensionality reduction algorithm that retains spatial structure. We combine
the wavelet transformation with matrix factorization to select
spatially-varying genes. We extract a low-dimensional representation of these
genes. We consider Empirical Bayes setting, imposing regularization through the
prior distribution of factor genes. Additionally, We provide visualization of
extracted representation genes capturing the global spatial pattern. We
illustrate the performance of our methods by spatial structure recovery and
gene expression reconstruction in simulation. In real data experiments, our
method identifies spatial structure of gene factors and outperforms regular
decomposition regarding reconstruction error. We found the connection between
the fluctuation of gene patterns and wavelet technique, providing smoother
visualization. We develop the package and share the workflow generating
reproducible quantitative results and gene visualization. The package is
available at https://github.com/OliverXUZY/waveST.
