Single-cell RNA sequencing (scRNA-seq) allows transcriptional profiling, and cell-type annotation of individual cells. However, sample preparation in typical scRNA-seq experiments often homogenizes the samples, thus spatial locations of individual cells are often lost. Although spatial transcriptomic techniques, such as in situ hybridization (ISH) or Slide-seq, can be used to measure gene expression in specific locations in samples, it remains a challenge to measure or infer expression level for every gene at a single-cell resolution in every location in tissues. We describe Laplacian Linear Optimal Transport (LLOT), a biologically interpretable method to integrate single-cell and spatial transcriptomics data to reconstruct missing information at a whole-genome and single cell resolution. LLOT has two essential features. First, it can recognize differences between datasets and correct platform effects efficiently based on a linear map. Second, it can handle complex spatial structures of tissues. We benchmarked LLOT against several other methods on real datasets. The results showed that LLOT consistently outperformed others in predicting spatial expressions and locations for single cells.