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
Signaltonoise radio (SNR)
D Î Â
2x2
Symmetric positive semideﬁnite 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) Firstorder differential of the edge magnitude along the xaxis
f
i, j
Noisefree 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 graylevel 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
/Ö2
_
Interobserver 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
Get Despeckle Filtering Algorithms and Software for Ultrasound Imaging now with O’Reilly online learning.
O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.