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Estimation of acoustic impedance from multiple ultrasound images with application to spatial compounding

TL;DR: This paper investigates reconstruction of the acoustic impedance from ultrasound images for the first time by combining multiple images to improve the estimation and uses phase information to determine regions of high reflection from an ultrasound image.
Abstract: Reflection of sound waves, due to acoustic impedance mismatch at the interface of two media, is the principal physical property which allows visualization with ultrasound. In this paper, we investigate reconstruction of the acoustic impedance from ultrasound images for the first time. Similar to spatial compounding, we combine multiple images to improve the estimation. We use phase information to determine regions of high reflection from an ultrasound image. We model the physical imaging process with an emphasis on the reflection of sound waves. The model is used in computing the acoustic impedance (up to a scale) from areas of high reflectivity. The acoustic impedance image can either be directly visualized or be used in simulation of ultrasound images from an arbitrary point of view. The experiments performed on in-vitro and in-vivo data show promising results.

Summary (4 min read)

1. Introduction

  • Ultrasound (US) has many advantages in comparison to other imaging modalities which has lead to its widespread use in clinical practice; it is (i) harmless at low power, (ii) portable, (iii) a real-time modality, and (iv) most importantly, cost effective.
  • Spatial compounding of several views, acquired 1Capacitive Micromachined Ultrasound Transducer from different positions, helps to reduce these shortcomings.
  • The prerequisite for spatial compounding is to know the relative positions of the acquired images.
  • Therefore, multi-angle compounding with beam steering is typically performed, where the probe remains fixed [22].
  • From each image, the authors will reconstruct an acoustic impedance image, which they subsequently average to get an estimation for the whole imaged area, see Figure 1.

1.1. Clinical Value of Compounding

  • The clinical value of US compounding is mainly a result of increased quality and extended FOV of the images presented to the physician.
  • When scanning the same region from different positions, speckle noise, which is direction dependent, can be reduced and therefore the SNR is improved [22].
  • Grau et al. [8] work on the combination of several acquisitions from different positions of the heart.
  • Third, size and distance measurements of large organs are possible [14].
  • And last, due to the increased features in the compounded view, specialists that are used to other modalities can better understand the spatial relationship of anatomical structures [10]; helping to bridge the gap between the modalities and making it easier to convey sonographic findings to other experts.

1.3. Outline

  • The authors will present a new approach for compounding, based on the estimation of acoustic impedance of the depicted region.
  • This has the advantage that the av- eraging becomes a less complex task, because the acoustic impedance images are less view-dependent than the original US images.
  • Once the acoustic impedance image is estimated, the authors can either present it directly or simulate ultrasound images from an arbitrary position.
  • The authors describe the physical process of ultrasound imaging, their ultrasound model, and the actual estimation in Section 2.
  • The authors experiments together with the results are shown in Section 3.

2. Method

  • Core to their method is the estimation of the acoustic impedance of the region depicted in the ultrasound image.
  • As the authors will see, acoustic impedance images are related to CT attenuation values expressed in Hounsfield units and no longer exhibit view-dependent artifacts and emphasized interface boundaries as in ultrasound images.
  • Having the acoustic impedance images zi from all views, the creation of a global acoustic impedance image z for the whole imaging scenario is possible.

2.1. Maximum Likelihood Estimation

  • The acoustic impedance estimation can be formulated as a maximum likelihood (ML) estimation.
  • (1) The likelihood function, which indicates how well the simulated US images.
  • In order to proceed with the ML estimation arg maxz L(z), the authors have to choose a distribution for the noise.

2.2. Physics of Ultrasound

  • In order to be able to estimate the acoustic impedance from an ultrasound image, the authors need a model of the physical imaging process.
  • Scattering and absorption affect attenuation, which characterizes the amplitude reduction as the wave propagates through a medium.
  • Ultrasound imaging can then be described by the reflection at tissue interfaces and the exponential loss of intensity within the tissue.
  • The authors can directly use this model without the need for a mapping.
  • The intensity is calculated recursively starting from the initial intensity of a sound beam I(0) by I(x) = I(x−∆d) · ρ(x).

2.3. Acoustic Impedance Estimation

  • The authors are going to describe the steps for acoustic impedance estimation.
  • First, the images are filtered to reduce speckle.
  • Second, the authors extract the phase information from the images to identify regions of high reflectivity.
  • Third, the authors use these regions to reconstruct the impedance for each image, and finally they find the global impedance estimation by averaging acoustic images obtained from each ultrasound image.

2.3.1 Filtering

  • Dealing with speckle in US images depends on the application.
  • In the majority of cases, speckle is treated as noise, which has to be removed before further processing the images.
  • In a recent work, however, Housden et al. [11] use speckle for the registration of consecutive slices in freehand ultrasound.
  • Also for acoustic impedance estimation, the authors focus on the regions with high reflectivity and want to ignore speckle from homogeneous parts in between.
  • A multitude of approaches for speckle reduction can be found in the literature such as Gaussian filtering, coherence-enhancing diffusion filtering, and despeckling filters based on the envelope of the US image [6].

2.3.2 Phase Calculation

  • Core to the acoustic impedance estimation is the identification of regions with high reflectivity, indicating a change in acoustic impedance.
  • For 1-D signals the phase is constructed from the original signal and its Hilbert transform.
  • There are different approaches to extend this concept to N -D.
  • The monogenic signal provides us with information about the phase and orientation of each pixel, see Figure 2(b) for an example.
  • The authors threshold the phase image, to get a mask, see Figure 2(c), to extract the reflectivity part from the ultrasound image.

2.3.3 Acoustic Impedance Calculation

  • Coming back to the ML formulation of their estimation in Equation (5), the authors see that the reflectivity term in Equation (14) exactly performs the wanted simulation when fo- cusing on the reflection.
  • The TGC compensates for attenuation of the ultrasound signal received from the tissue interfaces that are farther away from the ultrasound transmitter; simulating that everywhere in the image the same incident intensity is present.
  • The authors ignored the intensity term for the estimation in Equation (16).
  • This is sufficient for visualization and US simulation.
  • Since the authors estimate the acoustic impedance per scanline, an averaging with neighboring scanlines while propagating the values between the interfaces leads to smoother estimations, see Figure 2(e).

2.3.4 Compounding Acoustic Impedance Images

  • In section 1.2, the authors argued that compounding of ultrasound images is not a trivial task.
  • In contrast, compounding of estimated acoustic impedance images is straightforward because these images hold a correspondence between intensity value and tissue type.
  • The global acoustic impedance image z is consequently the mean of the estimates zi at each pixel position.
  • Problems can still occur when structures with high acoustic impedance such as bones cause occlusion in the underlying region.
  • For the detection of occlusions, the intensity term in Equation (13) can be used, to make a reliable compounding possible.

2.4. Visualization

  • Once the global acoustic impedance image z is estimated, the authors have to find ways to visualize it for the physician.
  • One possibility would be to directly present the acoustic impedance image, but this may be of limited clinical value, because physicians are not used to these images and may have problems interpreting them.
  • A better way may be to create artificial ultrasound views.
  • It has the advantage, that US views can be simulated that were initially not recorded, and from positions that are physically not possible, e.g. below the skin.
  • The authors use a recently introduced method by Shams et al. in [18], designed for simulating ultrasound images from CT data, to simulate US images from acoustic impedance, see Figure 8(h) for an example.

3. Results

  • The authors present results for the acoustic impedance estimation for three data sets.
  • Then, the phase is calculated on the filtered image, where the authors use a wavelength of 250mm for the log-Gabor filter, see Figure 2(b).
  • Determining the threshold is not critical and the authors performed all their experiments with a value of 0.7.
  • In Figures 4 and 5 the estimation steps for both forearm images are shown.
  • Finally, the authors use the global impedance image to simulate an ultrasound image, see Figure 8(h), with the same method they originally used to simulate the US images from CT.

4. Discussion

  • For the US image of the clay model, the authors were able to identify the interface and consequently make an estimation of the acoustic impedance.
  • The images of the forearm are pretty noisy, making an exact extraction of the parts with high reflectivity difficult.
  • The extraction of the bone, which is depicted as the half-round structure on the lower left, was correct.
  • In the acoustic impedance estimation of the first forearm the authors can see that the calculation becomes difficult when structures seem to split, as it is the case on the upper right side of the bone.
  • The authors simulated an ultrasound image from the global estimate at 0◦ rotation, to make it comparable to the original US images, but they could have simulated this from an arbitrary position.

5. Conclusion

  • The authors have presented a method to estimate acoustic impedance from multiple ultrasound images.
  • The key to the acoustic impedance calculation is to have a model from the physical imaging process to be able to analyze US images.
  • The authors proposed a phase-based image analysis to extract regions of high reflection from the image.
  • Based on this estimation, the authors are able to simulate US images from arbitrary positions.
  • It would, however, be helpful to integrate further data in the estimation process coming from RF, elastography, and speckle analysis, to make it more reliable.

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Estimation of Acoustic Impedance from Multiple Ultrasound Images
with Application to Spatial Compounding
Christian Wachinger
1
, Ramtin Shams
2
, Nassir Navab
1
1
Computer Aided Medical Procedures (CAMP), Technische Universit
¨
at M
¨
unchen, Germany
2
Research School of Information Sciences and Engineering (RSISE), The Australian National University
wachinge@in.tum.de, ramtin.shams@anu.edu.au, navab@in.tum.de
Abstract
Reflection of sound waves, due to acoustic impedance
mismatch at the interface of two media, is the principal
physical property which allows visualization with ultra-
sound. In this paper, we investigate reconstruction of the
acoustic impedance from ultrasound images for the first
time. Similar to spatial compounding, we combine multiple
images to improve the estimation. We use phase information
to determine regions of high reflection from an ultrasound
image. We model the physical imaging process with an em-
phasis on the reflection of sound waves. The model is used
in computing the acoustic impedance (up to a scale) from
areas of high reflectivity. The acoustic impedance image
can either be directly visualized or be used in simulation
of ultrasound images from an arbitrary point of view. The
experiments performed on in-vitro and in-vivo data show
promising results.
1. Introduction
Ultrasound (US) has many advantages in comparison to
other imaging modalities which has lead to its widespread
use in clinical practice; it is (i) harmless at low power, (ii)
portable, (iii) a real-time modality, and (iv) most impor-
tantly, cost effective. The recent introduction of 2D array
US transducers in the market makes further applications
possible, due to the instantaneous acquisition of ultrasound
volumes. Furthermore, the next generation of transducers
with CMUT
1
technology offers superior and efficient vol-
umetric imaging at a lower cost. However, ultrasound has
a number of disadvantages including: (i) a limited field-
of-view (FOV), (ii) occlusions behind structures with high
acoustic impedance, and (iii) a low singal-to-noise ratio
(SNR). Spatial compounding of several views, acquired
1
Capacitive Micromachined Ultrasound Transducer
Multiple
US Views
Acoustic
Impedance
Simulated
Ultrasound
Figure 1. Schematic illustration of spatial compounding with
acoustic impedance estimation. First, the impedance is estimated
from multiple ultrasound images. Second, an ultrasound image is
simulated from an arbitrary point of view.
from different positions, helps to reduce these shortcom-
ings.
The prerequisite for spatial compounding is to know the
relative positions of the acquired images. This can either be
obtained by tracking the ultrasound transducer or by image
registration. When working with 2D US images compound-
ing from different positions poses a problem, because all the
scans have to be in one plane. Therefore, multi-angle com-
pounding with beam steering is typically performed, where
the probe remains fixed [22]. Moving to 3D imaging, com-
pounding from different positions offers much more flexi-
bility, inspiring several groups to work on this subject e.g.
[6, 20]. In the following, we assume that we know the align-
ment of the images, and focus on how to combine their
intensity information. As we will discuss later in this re-
1
978-1-4244-2340-8/08/$25.00 ©2008 IEEE

port, combining ultrasound images is non-trivial due to the
highly view-dependent nature of the ultrasound. We will
introduce a novel approach, which is based on the estima-
tion of the acoustic impedance of the imaged scene. From
each image, we will reconstruct an acoustic impedance im-
age, which we subsequently average to get an estimation
for the whole imaged area, see Figure 1. These images can
either be directly presented to the physician or can be used
in simulation of ultrasound images from an arbitrary point
of view. To the best of our knowledge, this is the first time
that acoustic impedance is reconstructed from multiple ul-
trasound images.
1.1. Clinical Value of Compounding
The clinical value of US compounding is mainly a re-
sult of increased quality and extended FOV of the images
presented to the physician. When scanning the same re-
gion from different positions, speckle noise, which is direc-
tion dependent, can be reduced and therefore the SNR is
improved [22]. Moreover, occlusion artifacts below struc-
tures with high acoustic impedance can be removed and
the boundary continuity is enhanced. The positive ef-
fects of spatial compounding for diagnosis of atheroscle-
rotic plaques [12, 13] and breast cancer [2] have already
been reported. It also helps for administering epidural anes-
thesia by especially improving the depiction of key struc-
tures such as ligamentum flavum and epidural space [19].
Grau et al. [8] work on the combination of several acquisi-
tions from different positions of the heart. It is not possible
to depict the whole heart in a single acquisition, however,
scans from particular acoustic windows can be acquired to
show specific cardiac structures. The combination of these
acquisitions into a single volume can be of great benefit in
clinical practice.
The extended FOV is also of clinical value. First, sono-
graphers have the flexibility to visualize anatomical struc-
tures from a variety of different angles [17]. Second, the
spatial relationship among structures that are too large for a
single volume is easier to understand [14]. Third, size and
distance measurements of large organs are possible [14].
Fourth, individual structures within a broader context can
be identified by having an image of the whole examination
area [4]. And last, due to the increased features in the com-
pounded view, specialists that are used to other modalities
can better understand the spatial relationship of anatomi-
cal structures [10]; helping to bridge the gap between the
modalities and making it easier to convey sonographic find-
ings to other experts.
1.2. Related Work
The major problem in compounding ultrasound images,
is the combination of US intensity values from different
scans. If we were dealing with several computed tomog-
raphy (CT) images of the same object, the compounding
could be done by calculating the mean value. The dominant
features of ultrasound due to reflection and attenuation are,
however, view-dependent. Averaging intensity values is not
optimal because strong echoes from small incident angles
(transducer perpendicular to the surface) would be degraded
by weak echoes from large incidence angles. Therefore,
in the literature, several methods for spatial compounding
have been proposed, which we are going to discuss shortly.
Wilhjelm et al. [22] use multi-angle spatial compound-
ing with beam steering, for which the transducer stays at the
same spatial location. They were able to reduce the angle
dependency and speckle noise by combining multiple im-
ages. They compared a number of methods for compound-
ing including mean, median, root-mean-squared value, and
geometric mean. The highest SNR was achieved when us-
ing the mean method. In a recent work also based on beam
steering, Tran et al. [19] improved the spatial compounding
by using a combination of median- and gradient-based ap-
proaches. The median is used if at a certain location more
than half of the images have a high feature-content, other-
wise the gradient-weighted average is calculated. The prob-
lem we see with this approach is the use of thresholding to
decide whether a pixel has a high feature-content or not. Be-
har et al. [3] propose a new method for spatial compounding
by using three ultrasound transducers simultaneously. The
transducer in the middle acts as sender and receiver, the re-
maining two only act as receiver. With their method they
were able to improve visibility, detectability, and lateral res-
olution. During their experiments, various averaging meth-
ods were investigated, with the best results for the averaging
of intensities.
Leotta and Martin [15] propose a weighting scheme
based on the incidence angle of the ultrasound beam on a
reflecting surface. This technique leads to significantly im-
proved results in comparison to using the mean value, but is
based on an initial fitting of a surface to the data, which is a
challenge for complex images. Grau et al. [8] use multiscale
information about local structure definition and orientation
to weight the contributions of different images. The way
they obtain these image characteristics is by calculating the
image phase, which is invariant to image contrast being par-
ticularly interesting for US images. While this approach is
very interesting for image registration [7], the compounding
is rather cumbersome [8]. As can be seen, ultrasound com-
pounding is a non-trivial exercise and still an active field of
research.
1.3. Outline
In this article, we will present a new approach for com-
pounding, based on the estimation of acoustic impedance
of the depicted region. This has the advantage that the av-

eraging becomes a less complex task, because the acoustic
impedance images are less view-dependent than the orig-
inal US images. Once the acoustic impedance image is
estimated, we can either present it directly or simulate ul-
trasound images from an arbitrary position. We describe
the physical process of ultrasound imaging, our ultrasound
model, and the actual estimation in Section 2. Our experi-
ments together with the results are shown in Section 3.
2. Method
Core to our method is the estimation of the acoustic
impedance of the region depicted in the ultrasound image.
As we will see, acoustic impedance images are related to
CT attenuation values expressed in Hounsfield units and
no longer exhibit view-dependent artifacts and emphasized
interface boundaries as in ultrasound images. Having the
acoustic impedance images z
i
from all views, the creation
of a global acoustic impedance image z for the whole imag-
ing scenario is possible.
2.1. Maximum Likelihood Estimation
The acoustic impedance estimation can be formulated
as a maximum likelihood (ML) estimation. Therefore, we
have to define an US simulation function s, producing one
of the n simulated US images
ˆ
U = {ˆu
1
, . . . , ˆu
n
}, by taking
the corresponding transformation in T = {T
1
, . . . , T
n
} and
the acoustic impedance image z:
s : (z, T
i
) 7− ˆu
i
. (1)
The likelihood function, which indicates how well the sim-
ulated US images
ˆ
U match the real ones U = {u
1
, . . . , u
n
},
is
L(z) = P (U|z, T , ε) (2)
=
Y
i
P (u
i
|z, T
i
, ε) (3)
=
Y
i
P (u
i
s(z, T
i
) = ε), (4)
with the random variable ε modeling the noise and the as-
sumption of independent US images. In order to proceed
with the ML estimation arg max
z
L(z), we have to choose
a distribution for the noise.
Ultrasound speckle, in general, has a Rayleight distribu-
tion, however since we remove speckle as a preprocessing
step, a Gaussian distribution to model the noise in the im-
ages is more appropriate, which leads to the following least-
squares formulation
log L(z)
1
n
n
X
i=1
(u
i
s(z, T
i
))
2
. (5)
In the next section we will describe details of ultrasound
imaging to derive s.
Tissue 1 Tissue 2
Incident
Transmitted τ
Ultrasound
Transducer
Reflected ρ
Figure 3. Reflection and transmission of sound wave after hitting
an interface. The relative intensities are determined by the acoustic
impedances of the tissues.
2.2. Physics of Ultrasound
In order to be able to estimate the acoustic impedance
from an ultrasound image, we need a model of the physical
imaging process. A detailed description of ultrasound ph-
ysiscs can be found in [9]. Ultrasound waves are emitted
into the body to interact with the tissue, and the results are
presented for diagnosis in the form of reflected ultrasound
waves. There are many types of interactions, but the most
important ones, we are focusing on, are: reflection, scatter-
ing, and absorption. If the ultrasound beam hits an interface
between two tissues with different acoustic impedances, Z
1
and Z
2
, at normal incidence, part of the beam is reflected,
expressed by the reflection coefficient ρ:
ρ =
Z
2
Z
1
Z
2
+ Z
1
2
. (6)
The transmission coefficient τ is then given by:
τ = 1 ρ =
4 · Z
2
· Z
1
(Z
2
+ Z
1
)
2
. (7)
This type of reflection is called specular reflection (see
Fig. 3). One speaks of diffuse reflection if the beam is
reflected in multiple directions, happening when a rough-
surfaced interface is hit.
Scattering is responsible for providing the internal struc-
ture of the tissue and occurs when the beam hits interfaces
smaller than the size of its wavelength. Each of these scat-
terers reflects sound in all directions, causing speckle. Ab-
sorption, as well as scattering, is frequency dependent and
follows an exponential function
P (x) = P
max
· e
αx
(8)
with P
max
the initial sound pressure, P (x) the pressure af-
ter traversed distance x, and α the absorption coefficient.
Scattering and absorption affect attenuation, which char-
acterizes the amplitude reduction as the wave propagates

(a) Original US image (b) Phase image (c) Threshold of phase image (d) Impedance estimation (e) Smooth imp. estimation
Figure 2. Processing steps for acoustic impedance estimation of a clay model.
through a medium. Attenuation can also be described by an
exponential function similar to Equation (8), only replacing
the absorption coefficient α by an attenuation coefficient β,
which is the sum of the scattering and absorption coeffi-
cients.
Ultrasound imaging can then be described by the reflec-
tion at tissue interfaces and the exponential loss of inten-
sity within the tissue. Wein et al. [21], propose a model to
simulate US from CT, by mapping CT Hounsfield units to
acoustic impedance values. We can directly use this model
without the need for a mapping. Following the model, a
simulated ultrasound image ˆu is made up from a reflection
part r, an echogeneity part e, and a constant part, weighted
with parameters ω
i
ˆu(x) = ω
1
· r(x) + ω
2
· e(x) + ω
3
. (9)
Like mentioned, we focus on the regions of high reflec-
tion, where the echogeneity can be ignored. The intensity of
the sensed reflected signal R at a position x is calculated by
running along the scan line with direction d and evaluating
R(x) =
I
2
(x)
I(0)
cos
m
ϕ(x)
z(x) z(x d)
z(x) + z(x d)
2
(10)
with I(x) the intensity of the sound beam and ϕ(x) the in-
cidence angle at position x. The distance between scan line
points is indicated by d. The exponent m models the het-
erogeneity of the interface. The reflection coefficient, see
Equation (6), is then
ρ(x) =
z(x) z(x d)
z(x) + z(x d)
2
. (11)
The incidence angle, which is the angle between the US
beam and the normal of the surface, is calculated with the
scalar product
cos ϕ(x) =
d.
z(x)
|∇z(x)|
(12)
where is the spatial derivative operator. The intensity is
calculated recursively starting from the initial intensity of a
sound beam I(0) by
I(x) = I(x d) · ρ(x). (13)
Finally, a log-compression is applied to the images, so that
the reflectivity of the US images r(x) is
r(x) =
log(1 + a · R(x))
log(1 + a)
(14)
with a parameterizing the log-compression. We will use
these equations that describe the simulation of the reflectiv-
ity part of ultrasound images to reconstruct the impedance
in Section 2.3.3.
2.3. Acoustic Impedance Estimation
In this section, we are going to describe the steps for
acoustic impedance estimation. First, the images are filtered
to reduce speckle. Second, we extract the phase informa-
tion from the images to identify regions of high reflectivity.
Third, we use these regions to reconstruct the impedance for
each image, and finally we find the global impedance esti-
mation by averaging acoustic images obtained from each
ultrasound image.
2.3.1 Filtering
Dealing with speckle in US images depends on the appli-
cation. In the majority of cases, speckle is treated as noise,
which has to be removed before further processing the im-
ages. In a recent work, however, Housden et al. [11] use
speckle for the registration of consecutive slices in freehand
ultrasound. In compounding, where we want to average
image information from different viewing angles, speckle
patterns are mostly uncorrelated [6]. Also for acoustic
impedance estimation, we focus on the regions with high
reflectivity and want to ignore speckle from homogeneous
parts in between. A multitude of approaches for speckle
reduction can be found in the literature such as Gaussian
filtering, coherence-enhancing diffusion filtering, and de-
speckling filters based on the envelope of the US image [6].
We achieved good results with a median filter, which has
superior speckle reduction properties compared to Gaussian
smoothing [23].

(a) Original US image (b) Phase image (c) Threshold of phase image (d) Impedance estimation (e) Smooth imp. estimation
Figure 4. Processing steps for acoustic impedance estimation of the first forearm image.
(a) Original US image (b) Phase image (c) Threshold of phase image (d) Impedance estimation (e) Smooth imp. estimation
Figure 5. Processing steps for acoustic impedance estimation of the second forearm image.
2.3.2 Phase Calculation
Core to the acoustic impedance estimation is the identifi-
cation of regions with high reflectivity, indicating a change
in acoustic impedance. We use phase information for this
purpose because it provides us with structural information
independent of the brightness and contrast [8]. For 1-D sig-
nals the phase is constructed from the original signal and its
Hilbert transform. There are different approaches to extend
this concept to N -D. Here we will use the recently intro-
duced monogenic signal approach [5]. It uses a generaliza-
tion of the Hilbert transform, the Riesz transform, to calcu-
late phase information in N-D. The image is filtered by N
filters, which are given in the Fourier domain by
R
i
(f
1
, . . . , f
N
) =
f
i
q
P
N
j=1
f
2
j
(15)
with f
1
, . . . , f
N
the Fourier domain coordinates. We follow
[7] in applying log-Gabor filters prior to the calculation of
the monogenic signal of the image to extract frequency and
spatial localization. The monogenic signal provides us with
information about the phase and orientation of each pixel,
see Figure 2(b) for an example. We threshold the phase im-
age, to get a mask, see Figure 2(c), to extract the reflectivity
part from the ultrasound image.
2.3.3 Acoustic Impedance Calculation
Coming back to the ML formulation of our estimation in
Equation (5), we see that the reflectivity term in Equa-
tion (14) exactly performs the wanted simulation when fo-
cusing on the reflection. We will split up the direct estima-
tion of the global impedance z in Equation (5) and, instead,
estimate for each US image u
i
an acoustic impedance z
i
arg min
z
i
u
i
(x)
log (1 + a · (cos ϕ(x))
m
· ρ
z
i
(x))
log(1 + a)
2
.
(16)
In order to perform the optimization, we make the as-
sumption that the incidence angle for the impedance and
ultrasound image are roughly the same
cos ϕ(x) =
d.
z(x)
|∇z(x)|
d.
u(x)
|∇u(x)|
. (17)
Since the orientation of the interfaces in impedance and ul-
trasound image should be the same, this approximation is
reasonable. Considering, however, that US images are very
noisy, this can lead to problems. In our estimation frame-
work, we directly access the orientation information deliv-
ered by the phase calculation, which is very robust and ac-
curate, so that the approximation makes sense.
As shown in Equations (8) and (13), the intensity de-
creases as the ultrasound beam penetrates the tissue farther.
However, before the ultrasound images are output, a time-
gain compensation (TGC) is applied. The TGC compen-
sates for attenuation of the ultrasound signal received from
the tissue interfaces that are farther away from the ultra-
sound transmitter; simulating that everywhere in the image
the same incident intensity is present. Consequently, we ig-
nored the intensity term for the estimation in Equation (16).
The only term in Equation (16) that is still dependent on
the acoustic impedance is the reflection coefficient ρ
z
i
(x).

Citations
More filters
Patent
28 Jan 2011
TL;DR: A hand-held transducer can be used to assist in guiding a probe or locating a particular anatomical target in a subject as discussed by the authors, which can include an ultrasonic transducers located on or within a housing and configured to generate ultrasonic energy directed into tissue of a subject.
Abstract: A hand-held apparatus can be used to assist in guiding a probe or locating a particular anatomical target in a subject. The apparatus can include an ultrasonic transducer located on or within a housing and configured to generate ultrasonic energy directed into tissue of a subject and configured to receive a portion of the ultrasonic energy reflected by a target located within the tissue. In an example, the apparatus can include a motion tracking circuit configured to provide information indicative of a motion of the hand-held apparatus to the processor circuit, and a display configured to present information about a location of the target with respect to a portion of the hand-held apparatus, the information about the location determined by the processor circuit using the obtained information indicative of the ultrasonic energy reflected by the target and the information indicative of the motion of the hand-held apparatus.

35 citations

Journal ArticleDOI
TL;DR: It is demonstrated that the usage of an ultrasound specific similarity measure leads to better results for pairwise registration, and the highest robustness can be achieved by using simultaneous registration with the developed multivariate similarity measures.

34 citations


Cites background from "Estimation of acoustic impedance fr..."

  • ...[29] recently proposed a novel approach, based on the estimation of the acoustic impedance....

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Journal ArticleDOI
15 Feb 2017-Methods
TL;DR: This article is a review of registration algorithms for use between ultrasound images (monomodal image-based ultrasound registration) by presenting and discussing the complete published systems that have been validated for registration in specific anatomic regions.

32 citations

Patent
25 Apr 2012
TL;DR: An ultrasonic transducer can include a surface configured to provide or receive the ultrasonic energy, the surface including an area of greater than or equal to about 4λ2 as mentioned in this paper.
Abstract: An ultrasonic transducer element can configured to generate ultrasonic energy directed into tissue of a subject and configured to receive a portion of the ultrasonic energy reflected by a target located within the tissue. The ultrasonic transducer can include a surface configured to provide or receive the ultrasonic energy, the surface including an area of greater than or equal to about 4λ2, or the ultrasonic transducer element can be included in an array having a spacing between at least two adjacent ultrasound elements of less than or equal to about 1/2λ, and the array comprising an aperture that is at least approximately symmetrical in two axes. A three-dimensional representation of one or more of a location, shape, or orientation of at least a portion of the target can be presented via the display.

20 citations

Journal ArticleDOI
TL;DR: Results are presented suggesting that a fusion approach to MRF registration can produce accurate displacement fields much faster than standard approaches.

12 citations

References
More filters
Journal ArticleDOI
TL;DR: A geometric phase interpretation that is based on the relation between the 1-D analytic signal and the 2-D monogenic signal established by the Radon (1986) transform is introduced.
Abstract: This paper introduces a two-dimensional (2-D) generalization of the analytic signal This novel approach is based on the Riesz transform, which is used instead of the Hilbert transform The combination of a 2-D signal with the Riesz transformed one yields a sophisticated 2-D analytic signal: the monogenic signal The approach is derived analytically from irrotational and solenoidal vector fields Based on local amplitude and local phase, an appropriate local signal representation that preserves the split of identity, ie, the invariance-equivariance property of signal decomposition, is presented This is one of the central properties of the one-dimensional (1-D) analytic signal that decomposes a signal into structural and energetic information We show that further properties of the analytic signal concerning symmetry, energy, allpass transfer function, and orthogonality are also preserved, and we compare this with the behavior of other approaches for a 2-D analytic signal As a central topic of this paper, a geometric phase interpretation that is based on the relation between the 1-D analytic signal and the 2-D monogenic signal established by the Radon (1986) transform is introduced Possible applications of this relationship are sketched, and references to other applications of the monogenic signal are given

852 citations


"Estimation of acoustic impedance fr..." refers methods in this paper

  • ...Here we will use the recently introduced monogenic signal approach [5]....

    [...]

Journal ArticleDOI
TL;DR: The availability, low cost, and ease of examination makes ultrasound superior to MRI for follow-up of lesions and searching for healing problems such as as fibrosis, cystic haematomas, or myositis ossificans.
Abstract: Muscles are among the soft tissues one of the best adapted to ultrasound examination. In fact, it was the first imaging available for the evaluation of muscle disease. The availability, low cost, and ease of examination makes ultrasound superior to MRI for follow-up of lesions and searching for healing problems such as as fibrosis, cystic haematomas, or myositis ossificans. When dealing with fresh traumatic muscle lesions, the main goal of ultrasound is to assess the presence of a muscle tear or not. Haematoma is the key sign of a muscle tear. The ideal time for the examination is between 2 and 48 h after the muscle trauma. Before 2 h, the haematoma is still in formation. After 48 h, the haematoma can be spread outside of the muscle. After healing, ultrasound can depict some complications such as a cystic lesion or myositis ossificans. Muscle atrophy, inflammation, avulsion and tumours are also good indications for ultrasound.

403 citations


"Estimation of acoustic impedance fr..." refers background in this paper

  • ...First, sonographers have the flexibility to visualize anatomical structures from a variety of different angles [17]....

    [...]

Book
01 Jan 1985
TL;DR: In this article, the authors present new chapters on colour flow imaging, haemodynamics, vascular ultrasound and pulsed wave spectral analysis, with sample problems and review questions throughout, and explain aspects of physics applied to ultrasound and provide the background knowledge needed to perform quality scans.
Abstract: Explains aspects of physics as applied to ultrasound and provides the background knowledge needed to perform quality scans. This text has new chapters on colour flow imaging, haemodynamics, vascular ultrasound and pulsed wave spectral analysis, with sample problems and review questions throughout.

304 citations


"Estimation of acoustic impedance fr..." refers background in this paper

  • ...A detailed description of ultrasound physiscs can be found in [9]....

    [...]

Journal ArticleDOI
TL;DR: Real-time spatial compound imaging was found to produce speckle reduction with improvement of tissue differentiation, increased conspicuity of low-contrast lesions, enhanced delineation of capsular margins and ducts, and improved depiction of internal architecture of solid lesions, as well as clearer visualization of cystic contents due to clutter reduction.
Abstract: To determine the role of real-time spatial compound imaging in breast ultrasound (US), 38 patients with a total of 50 benign changes (fibroadenomas, cysts, lactiferous duct dilatation) underwent both conventional B-mode US and real-time spatial compound imaging under standardized examination settings. Subsequently, images were reviewed independently by three readers experienced in breast US and evaluated according to a multistage scoring system with regard to the presence of artefacts, delineation of boundaries and depiction of internal structures. With significant reader concordance, real-time spatial compound imaging was found to produce speckle reduction with improvement of tissue differentiation, increased conspicuity of low-contrast lesions, enhanced delineation of capsular margins and ducts, and improved depiction of internal architecture of solid lesions, as well as clearer visualization of cystic contents due to clutter reduction. Preservation of central acoustic enhancement and lateral edge shadowing in cysts and fibroadenomas, however, was recorded better in conventional imaging.

120 citations


"Estimation of acoustic impedance fr..." refers background in this paper

  • ...The positive effects of spatial compounding for diagnosis of atherosclerotic plaques [12, 13] and breast cancer [2] have already been reported....

    [...]

Journal ArticleDOI
TL;DR: An algorithm to register apical and parasternal echocardiographic datasets that uses a new similarity measure, based on local orientation and phase differences, to guide registration, so that the effect of artifacts intrinsic to ultrasound images is minimized.
Abstract: Real-time 3-D echocardiography opens up the possibility of interactive, fast 3-D analysis of cardiac anatomy and function. However, at the present time its quantitative power cannot be fully exploited due to the limited quality of the images. In this paper, we present an algorithm to register apical and parasternal echocardiographic datasets that uses a new similarity measure, based on local orientation and phase differences. By using phase and orientation to guide registration, the effect of artifacts intrinsic to ultrasound images is minimized. The presented method is fully automatic except for initialization. The accuracy of the method was validated qualitatively, resulting in 85% of the cardiac segments estimated having a registration error smaller than 2 mm, and no segments with an error larger than 5 mm. Robustness with respect to landmark initialization was validated quantitatively, with average errors smaller than 0.2 mm and 0.5o for initialization landmarks rotations of up to 15o and translations of up to 10 mm.

119 citations


"Estimation of acoustic impedance fr..." refers background in this paper

  • ...In compounding, where we want to average image information from different viewing angles, speckle patterns are mostly uncorrelated [6]....

    [...]

  • ...A multitude of approaches for speckle reduction can be found in the literature such as Gaussian filtering, coherence-enhancing diffusion filtering, and despeckling filters based on the envelope of the US image [6]....

    [...]

Frequently Asked Questions (10)
Q1. What have the authors contributed in "Estimation of acoustic impedance from multiple ultrasound images with application to spatial compounding" ?

In this paper, the authors investigate reconstruction of the acoustic impedance from ultrasound images for the first time. Similar to spatial compounding, the authors combine multiple images to improve the estimation. The experiments performed on in-vitro and in-vivo data show promising results. 

When scanning the same region from different positions, speckle noise, which is direction dependent, can be reduced and therefore the SNR is improved [22]. 

The clinical value of US compounding is mainly a result of increased quality and extended FOV of the images presented to the physician. 

In their estimation framework, the authors directly access the orientation information delivered by the phase calculation, which is very robust and accurate, so that the approximation makes sense. 

Ultrasound (US) has many advantages in comparison to other imaging modalities which has lead to its widespread use in clinical practice; it is (i) harmless at low power, (ii) portable, (iii) a real-time modality, and (iv) most importantly, cost effective. 

And last, due to the increased features in the compounded view, specialists that are used to other modalities can better understand the spatial relationship of anatomical structures [10]; helping to bridge the gap between the modalities and making it easier to convey sonographic findings to other experts. 

The authors simulated an ultrasound image from the global estimate at 0◦ rotation, to make it comparable to the original US images, but the authors could have simulated this from an arbitrary position. 

This has the advantage that the av-eraging becomes a less complex task, because the acoustic impedance images are less view-dependent than the original US images. 

the authors have to define an US simulation function s, producing one of the n simulated US images Û = {û1, . . . , ûn}, by taking the corresponding transformation in T = {T1, . . . , Tn} and the acoustic impedance image z:s : (z, Ti) 7−→ ûi. 

In contrast, compounding of estimated acoustic impedance images is straightforward because these images hold a correspondence between intensity value and tissue type.