Biomedical Engineering Reference
In-Depth Information
l
n
/2
L
N
=32
a
n
=16
l
n
=8
L
N
=32
a
n
=16
l
n
=16
h
m
/2
Orientation
angle
(a.1)
(a.2)
0,0
L
N
=64
a
n
=32
l
n
=8
L
N
=64
a
n
=32
l
n
=16
Tiling of
Fourier Plane
(b.1)
(b.2)
(a)
(b)
Figure 6.12: (a) Orientation and oscillation frequency of brushlet analysis func-
tions in 2D. The size of each subquadrant in the Fourier plane determines the
resolution of the analysis function while the position of the subquadrant center
determines the orientation of the analysis function. (b) Illustration of selected
brushlet orientation and oscillation frequencies. Fourier plane size
L
N
, center
frequency
a
n
, and subintervals size
l
n
are provided for each 2D brushlet basis
function.
3D to demonstrate the advantage of extending the brushlet analysis to 3D as
illustrated in Fig. 6.13, for a set of six long-axis and six short-axis slices.
Qualitatively, it was observed that the third dimension improved the quality
of the denoised data in terms of spatial resolution at the cost of losing some
contrast. When compared to 2D denoising, 3D denoising produced smoother
features with better-localized contours. Specifically, small local artifacts not per-
sistent in adjacent slices were eliminated and inversely weak contours persistent
in adjacent slices were enhanced. This phenomenon can be best appreciated in
the short-axis examples where the resolution is the lowest.
Improving Denoising by Including Time: Results on a Mathemati-
cal Phantom.
To quantitatively evaluate potential denoising performance im-
provement brought about by including the temporal dimension, initial testing
was performed on a mathematical phantom. The phantom, plotted in Fig. 6.14,
consisted of an ovoid volume growing in time that schematically mimicked as-
pects of the left ventricle with an inner gray cavity surrounded by a thick white
