Signal Processing - May 2017 - 95

acquisition over several pulse emissions gives a signal sample with a rate
of 1 Tprf = fprf , which has a frequency of
fp =

2v z
2v
f = z,
m
c 0

(4)

directly proportional to the axial blood
velocity. Here m = c f0 is the wavelength
of the transmitted pulse. The frequency
content in the transmitted pulse is scaled
by the factor 2v z c and also reduces the
influence of scattering and attenuation by
this factor. Velocity estimation, thus, relies
on acquiring the flow signal over several pulse emissions and determining the
motion between pulse emissions for estimating the axial velocity.

Axial velocity estimation
Several methods for finding the axial
velocity have been introduced [1].
Spectral systems use short-time Fourier transform to determine the frequency content of x s (n d, i) for the sample
depth n d, and these systems show the
velocity distribution over time for a
single position in the blood vessel as
a spectral display [2]. An example of
such a display is shown in the left part
of Figure 1(a). The gray tone B-mode
image displays the anatomy, and the

broken yellow lines indicate the place
for finding the velocity distribution. In
this spectrogram, the brightness indicates the relative number of scatterers
moving at a given speed. The yellow
"wings" indicate the beam-to-flow
angle, which has to be compensated for
to yield the correct velocity magnitude. It
is therefore preferred to keep this angle
below 60c if possible to avoid large errors in the compensated velocities. This
display gives a quantitative measure of
velocity and is widely used in the clinic
to evaluate peak velocities, volume flow,
and resistive index for indicating resistance to flow in the vessel.
The velocity can also be directly
estimated by cross-correlating two consecutive signals and then determining
the time shift [3]:
R 12 (n d, k) = / x s (n d + n, i) x s
n

# (n d + n + k, i + 1)
= / x s (n d + n, i) x s
n

# (n d + n - n s + k, i)
= R 11 (n d, k - n s),
2v z (n d)
Tprf fs,
n s (n d) =
(5)
c
where n is the sample index. Here
R 12 (n d, k) is the cross-correlation func-

(a)

tion and R 11 is the autocorrelation of
the received signal, which has a unique
peak found at the lag k = n s. The velocity
is then
v z (n d) =

n s (n d)
c.
2fs Tprf

(6)

For roughly monochromatic signals
(long pulse emissions with four to eight
cycles), the phase shift between the two
signals can be determined using the lag
one autocorrelation of the signals [4].
Here it is needed to perform a Hilbert
transform, y s (n, i) = H {x s (n, i)}, on the
received signal to find the direction of the
motion. This phase shift is directly proportional to the velocity and is found by
v z (n d) = -

cfprf
4rf0

J Nc - 1
N
K / y s (n d, i + 1) x s (n d, i) O
K i=1
O
K
O
- x s (n d, i + 1) y s (n d, i) O
# arctan K N c - 1
,
K
O
1
x
n
i
x
n
i
(
,
+
)
(
,
)
/
d
s
d
s
K
O
K i=1
O
K + y (n , i + 1) y (n , i) O
s
d
s
d
L
P
where N c is the number of emissions to
average over.
The velocity can then be found as a
function of depth, when using eight to

(b)

figure 1. (a) A duplex ultrasound scan shows, at the left, the anatomic B-mode image. The yellow broken line indicates the position for velocity estimation and, at the
right, shows the spectral display of the velocity distribution as a function of time. The brightness indicates the relative number of scatterers moving at a certain speed.
(b) A color flow map where the gray tones indicate the anatomy and the red color indicates velocity toward the transducer and blue away from it. The images were
acquired from the carotid artery and jugular vein in the neck of a human volunteer.

IEEE Signal Processing Magazine

|

May 2017

|

95



Table of Contents for the Digital Edition of Signal Processing - May 2017

Signal Processing - May 2017 - Cover1
Signal Processing - May 2017 - Cover2
Signal Processing - May 2017 - 1
Signal Processing - May 2017 - 2
Signal Processing - May 2017 - 3
Signal Processing - May 2017 - 4
Signal Processing - May 2017 - 5
Signal Processing - May 2017 - 6
Signal Processing - May 2017 - 7
Signal Processing - May 2017 - 8
Signal Processing - May 2017 - 9
Signal Processing - May 2017 - 10
Signal Processing - May 2017 - 11
Signal Processing - May 2017 - 12
Signal Processing - May 2017 - 13
Signal Processing - May 2017 - 14
Signal Processing - May 2017 - 15
Signal Processing - May 2017 - 16
Signal Processing - May 2017 - 17
Signal Processing - May 2017 - 18
Signal Processing - May 2017 - 19
Signal Processing - May 2017 - 20
Signal Processing - May 2017 - 21
Signal Processing - May 2017 - 22
Signal Processing - May 2017 - 23
Signal Processing - May 2017 - 24
Signal Processing - May 2017 - 25
Signal Processing - May 2017 - 26
Signal Processing - May 2017 - 27
Signal Processing - May 2017 - 28
Signal Processing - May 2017 - 29
Signal Processing - May 2017 - 30
Signal Processing - May 2017 - 31
Signal Processing - May 2017 - 32
Signal Processing - May 2017 - 33
Signal Processing - May 2017 - 34
Signal Processing - May 2017 - 35
Signal Processing - May 2017 - 36
Signal Processing - May 2017 - 37
Signal Processing - May 2017 - 38
Signal Processing - May 2017 - 39
Signal Processing - May 2017 - 40
Signal Processing - May 2017 - 41
Signal Processing - May 2017 - 42
Signal Processing - May 2017 - 43
Signal Processing - May 2017 - 44
Signal Processing - May 2017 - 45
Signal Processing - May 2017 - 46
Signal Processing - May 2017 - 47
Signal Processing - May 2017 - 48
Signal Processing - May 2017 - 49
Signal Processing - May 2017 - 50
Signal Processing - May 2017 - 51
Signal Processing - May 2017 - 52
Signal Processing - May 2017 - 53
Signal Processing - May 2017 - 54
Signal Processing - May 2017 - 55
Signal Processing - May 2017 - 56
Signal Processing - May 2017 - 57
Signal Processing - May 2017 - 58
Signal Processing - May 2017 - 59
Signal Processing - May 2017 - 60
Signal Processing - May 2017 - 61
Signal Processing - May 2017 - 62
Signal Processing - May 2017 - 63
Signal Processing - May 2017 - 64
Signal Processing - May 2017 - 65
Signal Processing - May 2017 - 66
Signal Processing - May 2017 - 67
Signal Processing - May 2017 - 68
Signal Processing - May 2017 - 69
Signal Processing - May 2017 - 70
Signal Processing - May 2017 - 71
Signal Processing - May 2017 - 72
Signal Processing - May 2017 - 73
Signal Processing - May 2017 - 74
Signal Processing - May 2017 - 75
Signal Processing - May 2017 - 76
Signal Processing - May 2017 - 77
Signal Processing - May 2017 - 78
Signal Processing - May 2017 - 79
Signal Processing - May 2017 - 80
Signal Processing - May 2017 - 81
Signal Processing - May 2017 - 82
Signal Processing - May 2017 - 83
Signal Processing - May 2017 - 84
Signal Processing - May 2017 - 85
Signal Processing - May 2017 - 86
Signal Processing - May 2017 - 87
Signal Processing - May 2017 - 88
Signal Processing - May 2017 - 89
Signal Processing - May 2017 - 90
Signal Processing - May 2017 - 91
Signal Processing - May 2017 - 92
Signal Processing - May 2017 - 93
Signal Processing - May 2017 - 94
Signal Processing - May 2017 - 95
Signal Processing - May 2017 - 96
Signal Processing - May 2017 - 97
Signal Processing - May 2017 - 98
Signal Processing - May 2017 - 99
Signal Processing - May 2017 - 100
Signal Processing - May 2017 - 101
Signal Processing - May 2017 - 102
Signal Processing - May 2017 - 103
Signal Processing - May 2017 - 104
Signal Processing - May 2017 - 105
Signal Processing - May 2017 - 106
Signal Processing - May 2017 - 107
Signal Processing - May 2017 - 108
Signal Processing - May 2017 - 109
Signal Processing - May 2017 - 110
Signal Processing - May 2017 - 111
Signal Processing - May 2017 - 112
Signal Processing - May 2017 - Cover3
Signal Processing - May 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com