Robust Frequency-Selective Knowledge-Based Parameter Estimation for NMR Spectroscopy

In many magnetic resonance spectroscopy (MRS)
applications, one strives to estimate the parameters
describing the signal to allow for more precise knowledge
of the analyte. Typically, MRS signals are well
modelled as a sum of damped sinusoids that has
properties that are partly known a priori. FREEK, a
recently proposed subspace-based parameter estimation
method allows for inclusion of such prior knowledge.
More specifically, FREEK assumes that there is a constant
frequency spacing (say Δ) between the damped
sinusoids, which is exactly known. However, any errors
in this prior knowledge will affect the accuracy of the
estimates. Herein, we present an extension of FREEK,
making it robust to such errors by allowing Δ to lie
in a small interval and utilizing a robust estimate of
Δ in the estimation of the remaining parameters. The
proposed approach is numerically shown to provide
robust estimates of the sinusoidal parameters at various
noise levels in the presence of mismatch between the
actual and the assumed spacing.