Signal Processing - March 2016 - 114

Detecting bubble motion using
nonlinear Doppler processing

Table 1. Multipulse techniques.
Pulse Sequence

b

m

rsum (t)

PI

(1, e )

(1, 1)

/

AM

c 1, 1 m
2

(1, - 2)

/ Nn = 1 (1 - 2 1 - n) a n p n (t)

CPS

c 1, 1 e jr, 1 e jr m
2
2

(1, 1, 1)

/ Nn = 1 (1 + 2 1 - n e jnr) a n p n (t)

jr

MB destruction, but this comes at the
cost of a reduced image resolution.
Coded transmission techniques, such as
frequency encoding (chirp), were developed for radar systems for the conflicting requirements of simultaneous high
SNR and high-resolution performance.
A long pulse with an embedded code is
transmitted. After reception, the signal is
cross-correlated with the transmitted
pulse to detect and remove the code and
restore the spatial resolution in a process
called compression.
A nonlinear compression filter can
be used to selectively extract and

N
n=1

jnr

n

(1 + e ) a n p (t)

compress the SH from the received
echo of MBs [6]. While this combination of harmonic imaging and chirp
transmission improves the resolution
of the technique, side lobes can appear
due to the chirp compression and frequency overlapping. The method can
be improved by extracting the chirp
SH component in a space between the
time and frequency using the fractional
Fourier transform [7]. Furthermore,
pulse encoding is not limited to frequency encoding (chirp) and other
codes, such as Barker and Golay, can
also be used.

The measurement of MB motion can
provide insight about the flow conditions (fast versus slow) and is useful
for determining whether targeted bubbles are bound or free flowing. Multipulse sequences can be used to both
detect the existence of MBs, as previously described, and to provide motion
information. The Doppler equation
describes the frequency shift given by
the relative motion between a sound
source and an observer. In US imaging, it can be used to determine movement of objects such as red blood cells
or MBs. For the sake of simplicity, we
focus only on motion along the US
propagation direction. The frequency
shift of a linear scatter moving with
velocity v is given by

Tf =

2f0 v ,
c

(5)

Vessel

Vessel
Tissue
1 cm

1 cm

(a)

(b)
Attenuation Artifact

(c)

(d)

figure 3. Imaging artefact correction: (a) PI and (b) corrected PI images of a flow phantom with two vessels containing diluted suspension of MBs
(adapted from [9] with permission), where the yellow arrows point to the small vessel recovered by the artefact correction. An in vivo CEUS image of a
carotid artery with (c) attenuation artefact (yellow arrow) and (d) attenuation artefact corrected (adapted from [10] with permission).

114

IEEE Signal Processing Magazine

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March 2016

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Table of Contents for the Digital Edition of Signal Processing - March 2016

Signal Processing - March 2016 - Cover1
Signal Processing - March 2016 - Cover2
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Signal Processing - March 2016 - Cover3
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