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