Estimation of acoustic impedance from multiple ultrasound images with application to spatial compounding
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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...In compounding, where we want to average image information from different viewing angles, speckle patterns are mostly uncorrelated [6]....
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Frequently Asked Questions (10)
Q2. What is the way to improve the SNR?
When scanning the same region from different positions, speckle noise, which is direction dependent, can be reduced and therefore the SNR is improved [22].
Q3. What is the clinical value of US compounding?
The clinical value of US compounding is mainly a result of increased quality and extended FOV of the images presented to the physician.
Q4. What is the ML framework used to estimate the phase of the ultrasound image?
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.
Q5. What is the advantage of using ultrasound?
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.
Q6. What is the way to describe the acoustic relationship of anatomical structures?
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.
Q7. How did the authors simulate an ultrasound image from the global estimate?
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.
Q8. What is the advantage of averaging ultrasound images?
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.
Q9. how do the authors estimate the acoustic impedance of an ultrasound image?
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.
Q10. What is the acoustic impedance of the ultrasound image?
In contrast, compounding of estimated acoustic impedance images is straightforward because these images hold a correspondence between intensity value and tissue type.