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.