MR spectroscopic imaging (MRSI) is a unique, powerful modality for non-invasive metabolic studies. For example, in neuroimaging studies, MRSI is so far the only non-invasive way to map the concentrations of the metabolites of the brain (e.g., N-acetylaspartate (NAA), Choline and Creatine), which provide critical information about neuronal viability, cellular membrane synthesis and energy production. However, clinical and research applications of this technology have been developing very slowly. One reason for this situation is due to poor signal-to-noise ratio (SNR) associated with MRSI data. This paper addresses this long-standing problem using a novel and powerful denoising scheme called LORA (Low Rank Approximations). LORA exploits two low-rank properties of MRSI data, one due to partial separability (of spatio-temporal variations) and the other due to linear predictability (of temporal variations). By imposing these two low-rank properties, LORA provides a new principled way to perform spatiotemporal filtering effectively. LORA has been validated using both simulated and in-vivo experimental data, producing very impressive results (see an example below). LORA is particularly useful for high-resolution MRSI studies where SNR is a major limitation. It could also be used for spatiotemporal filtering in other imaging modalities.