We introduce AMARES (advanced method for accurate, robust, Noninteractive methods exist that are noniterative and and efficient spectral fitting), an improved method for accurately computationally efficient and which can be fully automatic. and efficiently estimating the parameters of noisy magnetic reso-A serious drawback however is the fact that only very limited nance spectroscopy (MRS) signals in the time domain. As a referprior knowledge can be incorporated in these algorithms and ence time domain method we take VARPRO. VARPRO uses a that the model function is restricted to a sum of complex simple Levenberg-Marquardt algorithm to minimize the variable exponentially damped sinusoids. Among this class of methprojection functional. This variable projection functional is derived ods are the algorithms based on Kumaresan-Tufts' linear from a general functional, which minimizes the sum of squared prediction (LP) method (1) combined with singular value differences between the data and the model function. AMARES decomposition (SVD) (2). Kung et al.'s state-space apminimizes the general functional which improves the robustness proach (3) combined with SVD (called HSVD (4)) is a of MRS data quantification. The newly developed method uses a
version of NL2SOL, a sophisticated nonlinear least-squares algo-more efficient and more accurate alternative to the LP methrithm, to minimize the general functional. In addition, AMARES ods as it circumvents the polynomial rooting and root selecuses a singlet approach for imposition of prior knowledge instead tion. Rapid and more accurate variants of the state-space of the multiplet approach of VARPRO because this greatly extends algorithms have been recently proposed (5-8), but the limithe possibilities of the kind of prior knowledge that can be invoked. tations to the imposition of prior knowledge about model Other new features of AMARES are the possibility of fitting echo function parameters are inherent to these types of methods. signals, choosing a Lorentzian as well as a Gaussian lineshape for On the other hand, interactive methods exist that are iteraeach peak, and imposing lower and upper bounds on the parametive, with more user-involvement, in some cases computaters. Simulations, as well as in vivo experiments, confirm the better tionally less efficient, but that do allow inclusion of prior performance of AMARES compared to VARPRO in terms of accuknowledge. The algorithms fit the data to the nonlinear racy, robustness, and flexibility. แญง 1997 Academic Press model function in a least-squares sense, leading to maximum likelihood parameter estimates in the case of white Gaussian noise. See (9) for an overview of time domain methods.