a
i, j
Additive noise component on pixel i, j
a
comp
,
b
comp
Logarithmic compression parameters
b
(s)
Snake stiffness of the energy functional
b
GVF
GVF snake rigidity parameter
C
Speckle index
CV% Coefficient of variation
cd(½Ñg½½), c
i, j
Diffusion coefficient
c
adsr
Speckle reducing anisotropic diffusion coefficient
c
Constant controlling the magnitude of the potential
c
s sin_1
, c
s sin_2
Constants used to calculate the SSIN
c
2
Positive weighting factor
G
Number of directions, which diffusion is computed
g
Signal-to-noise radio (SNR)
D Î Â
2x2
Symmetric positive semi-definite diffusion tensor representing the
required diffusion in both gradient and contour directions
D
f
Fractal dimension
D
Matrix used to calculated the image energy of the snake, E
image
(
n
)
D
viewing
Viewing distance
DR Dynamic range of input ultrasound signal
d(k) Wavelet coefficient for the wavelet filtering
Df
Frequency shift (Doppler frequency shift)
Dr
Distance between two pixels
Ñg
The gradient magnitude of image g(x,y)(gradient)
Ñg
i, j
Directional derivative (simple difference) at location i, j
f
1
... f
13
SGLDM texture measures from Haralick
f
x
(x,y) First-order differential of the edge magnitude along the x-axis
f
i, j
Noise-free signal ultrasound signal in discrete form (the new image)
on pixel i, j
f
Frequency of ultrasound wave
f
0
Transmitted frequency of ultrasound signal
List of Symbols
147
148 DESPECKLE FILTERING ALGORITHMS
feat_dis
i
Percentage distance
g
i, j
Observed ultrasound signal in discrete formulation after logarithmic
compression
g(x,y)
Observed ultrasound signal after logarithmic compression,
representing image intensity at location (x, y)
G Linear gain of the amplifier
G
s
* g
i, j
Image convolved with Gaussian smoothing filter
G
s
Gaussian smoothing filter
g
_
i
, f
_
i
Mean gravity of the searching pixel region in image g or f
g
max
and g
min
Maximum and minimum gray-level values in a pixel neighborhood,
respectively
Ha, kHz, and MHz Hertz, kilohertz, and megahertz, respectively
HX, HY
Entropies of p
x
and p
y
H
(k)
Hurst coefficients
H(x,y) Array of points of the same size for the HT
HD Hausdorff distance
h
s
Spatial neighborhood of pixel i, j
|h
s
|
Number of neighbors (usually four except at the image boundaries)
q
i
Phase shift relative to the insonated ultrasound wave
q
Angle between the direction of movement of the moving object and
the ultrasound beam
I Identity matrix
I
0
(x) Modified Bessel function of the first kind of order 0
I
1
- I
7
Echo boundaries describing the regions in carotid artery
IMT
mean
Mean value of the IMT
IMT
min
IMT minimum value
IMT
max
IMT maximum value
IMT
median
IMT median value
k
Coefficient of variation for speckle filtering
l
Wavelength of ultrasound wave
l
p
Lai and Chin snake energy regularization parameter, E
snake
(
n
)
l
d
Î Â
+
Rate of diffusion for the anisotropic diffusion filter
m
i1
and m
i2
Mean values of two classes (asymptomatic and symptomatic,
respectively)
LIST OF SYMBOLS 149
m/s and cm/s Meters per second and centimeters per second, respectively
m
Mean
N
Number of scatterers within a resolution cell
N
feat
Number of features in the feature set
n
i, j
Multiplicative noise component (independent of g
i, j
, with mean 0)
on pixel i, j
nl
i, j
Multiplicative noise component after logarithmic compression on
pixel i, j
n(s) Normal force tensor
x
i
Amount of ultrasound signal backscattered by scatterer i
p
x
(i )
ith entry in the marginal probability matrix obtained by summing
the rows of p(i, j)
Q
Mathematically defined universal quality index
R = 1 -
1
1 +
s
2
Smoothness of an image
Score_Dis
Score distance between two classes (asymptomatic, symptomatic)
s
e
=
s
IMT
2
_
Inter-observer error
s
max
Maximum pixel value in the image
s
2
Structural energy
s
IMT
IMT standard deviation
s
fg
Covariance between two images f and g
s
Standard deviation
s
2
Variance
s
3
Skewness
s
4
Kurtosis
s
i1
and
s
i2
Standard deviations of two classes (asymptomatic and symptomatic,
respectively)
2
s
2
Diffuse energy
s
n
Standard deviation of the noise
s
2
w
Variance of the gray values in a pixel window

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