Image Processing Reference
In-Depth Information
Solving Equation 12.21 or Equation 12.16 will lead to the same results.
However, in Equation 12.21, a fewer number of variables are involved even if
the functional is more complicated.
Following the same idea, a priori biochemical knowledge (e.g., known ampli-
tudes and damping ratios, and frequency shifts and common phases) can be
included in the functional as well. In fact, when prior knowledge can be expressed
as a set of constraints among parameters, these constraints are substituted in the
functional (either Equation 12.21 or Equation 12.16), thus reducing the dimension
of the parameter space. In this way, regardless of the existence of constraints
among parameters, an unconstrained NLLS optimization problem is always solved.
Several modified versions of the original approach have been presented, which
differ for the selected minimization algorithm [42,45-48] or for the kind of prior
knowledge included into the procedure [42,48,49]. An example of application of
the method proposed in Reference 42 is shown in Figure 12.4 .
12.6
CONCLUSIONS
A general overview of the common signal processing methods for metabolite
quantification in MRS is presented. Fundamentals of both time-domain methods
and frequency-domain approaches have been introduced in order to provide some
theoretical basis that may help the reader to appreciate the power of these tech-
niques and their correct applicability to the processing of MRS data. It is worth
noting that an optimal approach does not exist. Conversely, due to the variety of
MRS spectra characteristics, it is a common experience that different signal
processing methods (and models) must be employed for analyzing data acquired
from various tissues (brain, muscle, or liver) or different nuclei ( 1 H, 31 P, etc.).
The accuracy of the results depends on the correct match between the selected
model and characteristics of the experimental signals. A few multicenter studies
and review articles [21,22,50] have deeply compared the various signal processing
approaches and widely exploited the advantages and shortcomings of each
method. It is not the aim of this chapter to describe them in detail, but we hope
that the presented concepts could give a general picture of the peculiarities of
each method, stressing those aspects that make them suitable and attractive for
quantitative analysis of MRS data.
REFERENCES
1.
Gandian, D. (1995). NMR and Its Application to Living Systems. 2nd ed. Oxford:
Oxford University Press.
2.
de Certaines, J.D., Bovée, W.M.M.J., and Podo, F. (1992). Magnetic Resonance
Spectroscopy in Biology and Medicine . Oxford: Pergamon Press.
3.
Howe, F.A., Maxwell, R.J., Saunders, D.E., Brown, M.M., and Griffiths, J.R.
(1993). Proton spectroscopy in vivo, Magn. Res. Q. 9: 31-59.
4.
Falini, A., Calabrese, G., Origgi, D., Lipari, S., Triulzi, F., Losa, M., and Scotti,
G. (1996). Proton magnetic resonance spectroscopy in intracranial tumors: clinical
perspectives J. Neurol. 243: 706-714.
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