We introduce the KNOB-SVD (knowledge based singular
value decomposition)
method for exploiting prior knowledge in MR
spectroscopy based on the singular value decomposition (SVD) of
the data matrix. More specifically we assume that the MR data
is well modeled by the superposition of a given number of exponentially
damped 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 whose
dampings, frequencies and amplitudes may in some cases be known to
satisfy the above type of relations, is used as a vehicle for describing
our SVD-based method throughout the paper. By means of numerical
examples we show that our method provides more accurate parameter
estimates than a commonly-used general-purpose SVD-based method
and a previously suggested prior knowledge-based SVD method.