Spatial transcriptomics (ST) technologies provide gene expression close to or even superior to single-cell resolution while retaining the physical locations of sequencing and often also providing matched pathology images. However, the expression data captured by ST technologies suffer from high noise levels, including but not limited to drop-outs as in regular single-cell RNA-sequencing (scRNA-seq). The extra experimental steps for preserving the spatial locations of sequencing could result in even more severe noises, compared to regular scRNA-seq. Fortunately, such noises could be largely removed by leveraging information from the physical locations of sequencing, and the tissue and cellular organization reflected by corresponding pathology images. In this work, we demonstrated the extensive levels of noise in ST data. We developed a mathematical model, named Sprod, to remove such noises based on latent space and graph learning of matched location and imaging data. We comprehensively validated Sprod and demonstrated its advantages over prior methods for removing drop-outs in scRNA-seq data. We further showed that, after adequately de-noising by Sprod, differential expression analyses, pseudotime analyses, and cell-to-cell interaction inferences yield significantly more informative results. In particular, with Sprod, we discovered 3-4 times more RNA transcripts that were actively transported in mouse hippocampus neurons. We also showed that the tumor cells at the tumor-stroma boundaries demonstrate differential transcriptomic features from the tumor cells in the central regions, caused by their interactions with the stroma/immune cells. Overall, we envision denoising by Sprod to become a key first step to empower ST technologies for biomedical discoveries and innovations.