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The use of low-rank approximation filters in the field of NMR is increasingdue to their flexibility and effectiveness. Despite their ability to reduce theMean Square Error between the processed signal and the true signal is wellknown, the statistical distribution of the residual noise is still undescribed.In this article, we show that low-rank approximation filters are equivalent tolinear filters, and we calculate the mean and the covariance matrix of theprocessed data. We also show how to use this knowledge to build a maximumlikelihood estimator, and we test the estimator's performance with a Montecarlosimulation of a 13C pyruvate metabolic tracer. While the article focuses on NMRspectroscopy experiment with hyperpolarized tracer, we also show that theresults can be applied to tensorial data (e.g. using HOSVD) or 1D data (e.g.Cadzow filter).

Statistical characterization of residual noise in the low-rank  approximation filter framework, general theory and application to  hyperpolarized tracer spectroscopy