Image Processing Reference
In-Depth Information
of phase-encoding steps. However, as shown in Equation 11.5, this improvement
is at the expense of acquisition time. The minimum accepted number of encoding
steps is usually considered to be eight (for the FFT algorithm, N must be a power
of two, unless zero filling is used).
Because the PSF shape is not rectangular and the PSF extends over many
voxels, Equation 11.14 implies that the signal measured at the given position
(the given voxel, in reality) is always contaminated by the signals from other
locations in the sample. This signal “bleeding” leads to the loss of localization
precision, and it is the determining factor for the resulting resolution of the
CSI experiment. In large samples with prevailing homogenous signal distri-
bution, the effects of the side lobes of PSF may, owing to the oscillatory
character of PSF, partially cancel each other out. However, because metabolites
are generally distributed in the sample nonuniformly, the existence of PSF
leads to the inaccurate determination of the signal distribution, and the recon-
structed signal s
rec
(t,
r
l′,m′,n′
) does not equal the true one, s (t,
r
l′,m′,n′
). Only a
potential contamination can be predicted from the PSF shape, because the final
contamination depends on the exact metabolite distribution.
The elimination of PSF by the deconvolution of the measured concentrations
into the known PSF and the true metabolite signal is not possible, because all
spectra in the CSI grid are never available with the sufficient quality and decon-
volution methods are very prone to noise. Alternatively,
a priori
information from
an MRI image can be used for more sophisticated reconstructions to diminish
PSF effects to some extent (45,46).
The existence of PSF explains the need for the suppression of subcutaneous
lipids in the scalp and other areas with spurious signals. Even if the relative
contributions of distinct voxels are small, the contamination by lipid signal can be
severe due to big differences in metabolite and fat concentrations (1:10
3
). Moreover,
because lipid resonances in distant areas are often shifted (owing to different
magnetic field strengths), signal bleeding usually results in the spoiling of the whole
spectral range.
11.3.4
K-
SPACE
W
EIGHTING
T
ECHNIQUES
For a fixed size of FOV, the profile of the PSF improves if the number of phase-
encoding steps is increased as depicted in
Figure 11.17
. However, due to time
constraints and sensitivity reasons, a compromise in the number of encoding steps
is necessary.
Even if the number of phase-encoding steps is limited, other possibilities
of improving the PSF shape are available. Because the FT of the product of
two functions is the convolution of their FT, multiplying measured k-space
data S (t,
k
l,m,n
) with a filter function will influence the resulting PSF. This
postacquisition k-space filtering, also called
apodization
, is realized by the
multiplication of the measured k-space data with symmetrical filters having
the maximal value in the center of the k-space and smoothly decreasing toward
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