Using prior knowledge in SVD-based parameter estimation for magnetic resonance spectroscopy--the ATP example

• We introduce the KNOB-SVD (knowledge based singularvalue decomposition)method for exploiting prior knowledge in MRspectroscopy based on the singular value decomposition (SVD) ofthe data matrix. More specifically we assume that the MR datais well modeled by the superposition of a given number of exponentiallydamped sinusoidal components, and that the dampings $\alpha_k$,frequencies $\omega_k$ and complex amplitudes $\rho_k$of some components satisfy the following relations:$\alpha_k = \alpha$ ($\alpha = \textrm{unknown}$),$\omega_k = \omega + (k-1) \Delta$ ($\omega = \textrm{unknown}$,$\Delta = \textrm{known}$), and $\rho_k = c_k \rho$($\rho = \textrm{unknown}$, $c_k = \textrm{known real constants}$).The ATP (adenosine triphosphate) complex,which has one triple peak and two double peaks whosedampings, frequencies and amplitudes may in some cases be known tosatisfy the above type of relations, is used as a vehicle for describingour SVD-based method throughout the paper. By means of numericalexamples we show that our method provides more accurate parameterestimates than a commonly-used general-purpose SVD-based methodand a previously suggested prior knowledge-based SVD method.

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