Image Processing Reference
In-Depth Information
higher-amplitude signal terms, are least affected by
), whereas later points, in
which signals are decayed below the noise level, are strongly attenuated. In this
case, improvement of SNR is made by broadening spectral lines, thus reducing
spectral resolution.
The windowing procedure can also be used for resolution improvement. In
fact, if
g
(
n
is chosen as negative, the decaying time of the FID is increased,
producing a narrowing of spectral lines. However, use of this technique needs
some care — if
d
0
is too negative, the latest point in the FID is highly amplified,
thus enhancing noise rather than signal and resulting in a prohibitively noisy
spectrum.
A compromise between enhancement of SNR and resolution is obtained by
combining the weighting function with negative
d
0
with another function decaying
to zero at the tail of the FID. The resulting weighting curve has a maximum
located in the early points of the FID. Usually, a combination of the exponential
and Gaussian function is used
d
0
2
gn
()
=
e
dn
e
(
dn
g
)
(12.6)
0
's to generate delta spectral
lines in the presence of true resonance, which are then convolved by the Gaussian
curve of Equation 12.6. The resulting spectrum will be composed of a summation
of Gaussian lines. For this reason, the latter operation is known as
In practice,
d
is chosen as close as possible to
d
0
k
Lorentz-Gauss
Transform.
The advantage is that the Gaussian lineshape, with the same half-
height line width of the Lorentzian one, has a narrow base, thus reducing overlap
of peaks and increasing resolution. Results of the Lorentz-Gauss transformation
are shown in Figure 12.2c . A weighting function decaying to zero at the end of
the FID can also be useful to smooth the truncation at the end of FID, if it has
not decayed to zero during acquisition (
).
Finally, windowing can be also used to reduce the influence of broad spectral
components. Here, the selected weighting function is
apodization
gn
()
=−
1
Ae dn
,
where
d
b
b
is much greater than the
d
's of the narrow signals of clinical interest. Because
k
d
of
these metabolite is then subtracted from the acquired FID data to remove them.
Results are shown in Figure 12.2d.
>>
d
's, the term
gn
()
=
e dn
enhances broadband metabolites. A fraction
A
b
b
k
12.3.3
R
U
R
EMOVAL
OF
NDESIRED
ESONANCE
The acquired MRS signal contains several resonance frequencies due to the
complexity of living systems and metabolism. However, only few of them have
clinical and diagnostic relevance. It is, therefore, desirable to remove unwanted
peaks, thus improving the readability of the spectrum, accuracy in parameter
estimation, and reducing the computational burden. The most straightforward
example of undesired resonance is the water peak in proton MRS. In fact, water
is largely diffused in living tissues and provides the most relevant contribution
to the
1
H-MRS FID.
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