Abstract
Recently, a method for estimating an exponentially decaying spectrum based on complex Kalman filter in combinaiton with decaying exponential window, what is called “apodization” in the field of NMR, has been proposed. The method can produce a high resolution spectrum from a noisy exponential decaying signal and enhance the signal-to-noise ratio in the spectrum, simultaneously.
We modify the method to estimate in vivo 31P -NMR spectra by means of dividing an FID into several segments and varying the effect of apodizaton fo each segment. We name these “segmented apodizaiton”. Furthermore, we introduce the forgetting factor, which is used in the recursive least square (RLS), into the complex Kalman filter and attempt to vary it in the filter operation corresponding to the apodization in each segment. we compare the segmentde apodization with the conventional one and examine the effect of the forgetting factor.
Simulations is performed using the signal which is generate d by the paramenters (T*2, peak area, frequency) of 31P-NMR spectrum acquired from a mouse tumor cell under 2 Tesla condition.
As a result, The forgetting factor is so effective to the estimation of in vivo 31P-NMR spectra. It is shown that one can estimate the spectrum more accurately using the segemented apodization by setting an adequate segmentation and adequate dumping rates.
