Sidelobe reduction for plane wave compounding with a limited frame number
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Abstract
Background
In ultrasound plane wave imaging (PWI), image details are often blurred by the offaxis artefacts resulting from high sidelobe. Recently plane wave compounding (PWC) is proposed as a promising technique for the sidelobe suppression in the PWI. However, its high demand for the frame number results in an obvious frame rate loss, which is intolerable in the ultrafast imaging modality. To reduce the number of frames required for compounding, coherence in the compounding frames should be exploited.
Methods
In this paper, we propose a global effective distancebased sidelobe suppressing method for the PWC with a limited frame number, where the global effective distance is introduced to measure the interframe coherence. Specifically, the effective distance is firstly computed by using a sparse representationbased algorithm. Then, the sidelobe localization is carried out on the basis of the effective distance. Finally, the targetdependent weighting factor is adopted to suppress the sidelobe.
Results
To assert the superiority of our proposed method, we compare the performances of different sidelobe reduction methods on both simulated and experimental PWC data. In case of 5 steering angles, our method shows a 19 dB reduction in the peak sidelobe level compared to the normal PWC in the point spread function test, and the contrast ratio is enhanced by more than 10% in both the simulation and phantom studies.
Conclusions
Consequently, the proposed method is convinced to be a promising approach in enhancing the PWC image quality.
Keywords
Sidelobe reduction Plane wave compounding Limited steering angles Effective distance Sparse representationAbbreviations
 CR
contrast ratio
 CNR
contrast to noise ratio
 DAS
delay and sum
 FWHM
full width at half maximum
 GPU
graphics processing unit
 IFCF
interframe coherence factor
 IUS
international ultrasonics symposium
 MSR
modified sparse representation
 MV
minimum variance
 PICMUS
plane wave imaging in medical ultrasound
 PSF
point spread function
 PSL
peak sidelobe level
 PWC
plane wave compounding
 PWI
plane wave imaging
 RF
radio frequency
 ROI
region of interest
 SNR
signal to noise ratio
 SVD
singular value decomposition
Background
The concept of ultrafast imaging using plane waves has been introduced in medical ultrasound for several years [1, 2]. In this modality, a plane wave is generated by applying flat delays to all elements of an ultrasound probe. The generated wave will insonify the whole area of interest. In this way, the plane wave imaging (PWI) allows the acquisition of one full ultrasound image from a single shot. Till now, the PWI has shown potential in a wide range of realtime applications, such as the ultrafast elastography, cardiac activity monitoring and dynamic micro flow imaging [3, 4, 5, 6].
One class of methods to reduce the sidelobe level in ultrasound imaging is to apply window apodization to the transducer array [7, 8]. Despite the ease of use, this kind of method has several drawbacks. First, the applied weighting values are fixed and independent of the depth and imaging target. Second, the weighted output may widen the mainlobe and affect the lateral resolution.
Another kind of approach is to calculate the beamforming weight vector on the receiving end. A good example is the minimum variance (MV) adaptive beamformer [9, 10]. In the MV, the weights are calculated by minimizing the power of the beamforming output subject to the constraint that the given response in the lookingdirection is lossless. This method also has some defects. First, the performance of the MV beamformer is dependent on the signaltonoise ratio (SNR) of the imaging scenario. This means that the MV beamformer is not so feasible for the PWI modality. Second, compared to the nonadaptive delayandsum (DAS) beamformer, the MV beamformer has heavier computation load, which is intolerable in the ultrafast ultrasound imaging modality.
Several methods have also been proposed to suppress the sidelobe in the ultrasound imaging. Zhang et al. [11] used the correlation coefficient of plane wave and spherical wave transmissions to weight the array signal. Considering the quick decline of the spherical wave energy during propagation, the validity of the method should be further verified. He et al. [12] solved an optimization problem to obtain the weight vector based on the nearfield response vector of a transducer array. They put more emphasis on the traditional linearscan imaging.
Recently, the concept of plane wave compounding (PWC) has been proposed to improve the imaging quality of the singleshot PWI [13, 14]. It has been proved that the sidelobe pattern is largely dependent on the steering direction [7]. The summation of beam formed data obtained by PWI transmissions with different steering angles results in an image quality similar to the conventional multifocus ultrasound imaging with a higher frame rate. It has been proved that the PWC can successfully suppress the sidelobe when the compounding frames are sufficient [13]. On this occasion, the PWI loses its frame rate advantage over a focused linearscan acquisition. To reduce the PWC transmissions, our group has developed a sidelobe reduction beamformer for the PWC based on the singular value decomposition (SVD) filter [15]. The key point is that the sidelobe artefacts from different angles have poor coherence [7]. This algorithm then regards the sidelobe as the highfrequency component among frames and then wipes it out. It works well when the steering angles are no less than 10.
In this paper, we propose a sidelobe suppressing method based on this new kind of distance, which is particularly effective for the PWC with a limited frame number. To the best of our knowledge, it is the first time that the effective distance is used as a coherence measure in the multiangle ultrasound imaging. Our method includes the following three steps. First, the effective distance within the compounding frames is calculated by using a sparse representationbased algorithm. Second, the region affected by high sidelobe is localized adaptively according to the calculated effective distance. Finally, a regionwise weighting factor is used to control the sidelobe. This new approach is assessed by simulation with the Field II program [20] and phantom experiments with a Verasonics system on a commercial phantom. Results showed that among the methods we tested, our proposed method performs best in terms of the imaging contrast and sidelobe suppression performance. In the meanwhile, the imaging resolution is unaffected.
The rest of the paper is organized as follows: the background of the PWC and the framework of the proposed method are presented in “Methods” section. Results of both simulated and phantom data are shown in “Results” section. In “Discussion” section, the comparison and discussion of the proposed method are presented. Finally, conclusions are given in “Conclusions” section.
Methods
In this section, we briefly introduce the background of the PWC at first. Then we explain the definition of the effective distance and show the use of the effective distance for the sidelobe suppression in the PWC scenario. After a short summary of our method, the setup of our experiments is given at the end of this section.
Plane wave compounding (PWC)
As the beam pattern is closely related to the steering angle, transmissions in the PWC correspond to different forms of sidelobe artefact, which have low coherence. The interframe coherence then acts as the key to solve the sidelobe reduction problem.
Effective distance and its calculation
Global effective distance
Using such effective distance in the feature selection methods has helped in finding the most discriminative features in data [21]. To the best of our knowledge, no previous studies have used such effective distance for the sidelobe suppression in the ultrasound imaging.
Sparse representationbased solution for the connectivity matrix \(\varvec{P}\)
To obtain the connectivity matrix \(\varvec{P}\), we turn to the sparse representation solution which is proven robust to the noise. In [22], Qiao et al. proposed a sparse reconstructive weight matrix based on a Modified Sparse Representation (MSR) framework. Results showed that a compact representation of data could be obtained by such a framework, thus we choose it as the solution in our method.
Sidelobe reduction using the modified effective distance
Modified effective distance for the PWC
In the PWC, it is important to obtain an overall rating of the interframe coherence. Through analogy, the nodes in Fig. 4 can be replaced by the envelope intensities from different angles in the PWC. The connectivity coefficient \(P_{mn}\) denotes the relative similarity between the sample n and the sample m in fraction. Considering the direction in the graph, the “arrows leaving the sample n” describes the probabilities of the sample n belonging to the other samples’ class in fraction, the sum of which always equals to one. The “arrows reaching the sample n” describes the level to which the other samples and the sample n are in the same class.
Sidelobe localization using the effective distance
Interframe coherence factor (IFCF)
Parameters selection in our method
Selection for \(ED_{g}\) thresholds \(\theta_{1} ,\theta_{2}\)
As analyzed in “Effective distance and its calculation” section, the connectivity coefficient \(P_{i,j}\) also denotes the ability of the envelop intensity from the frame \(j\) to represent the envelop intensity from the frame \(i\). For the position where the mainlobe energy dominates, the envelope intensities of the compounding frames are similar and have high coherence. On this occasion, the connectivity coefficients have the good capacity to represent all compounding frames, so the connectivity coefficient sums are all large. However, in the sidelobeaffected region, the connectivity coefficients vary with the steering angles, resulting in low coherence. As a consequence, the connectivity coefficients will generate a small minimum connectivity coefficient sum. The similar process of the coherence measure makes us relate \(ED_{g}\) to the wellknown correlation coefficient r. Hence, we referred to the relevant literatures [24, 25, 26] for the threshold selection, in which r < 0.25 usually represents weak correlation and r ≥ 0.75 represents strong correlation.
Thus, two thresholds \(\theta_{1} ,\theta_{2}\) for \(ED_{g}\) are set to 0.25 and 0.75 respectively in the present research.
Selection for weighting factors \(\alpha_{1} ,\alpha_{2} ,\alpha_{3}\)
We choose 0.2, 1, 1.2 as the weight factors \(\alpha_{1} ,\alpha_{2} ,\alpha_{3}\) for the sidelobeaffected targets, speckle and mainlobedominated targets respectively in our research. After log compression, the factors 0.2 and 1.2 are converted into − 15 and 1.5 dB. The reasons for our choice are as follows.
For the sidelobeaffected regions (e.g. anechoic lesions, trailing artefact), the signal power is expected to be suppressed. However, the weight factor needs to be greater than 0 in order to avoid the dark artefact around the strong scatterers. In our experiments, all images are shown with a dynamic range of 60 dB. Under ideal conditions, the hyperechoic points, the averaged speckle and the anechoic cysts correspond to 0, − 30, − 60 dB respectively. However, in practice, the intensities of the speckle and the cysts are enhanced due to the pollution of the sidelobe artefacts. We can roughly represent the sidelobe artefact intensity with the median between the speckle intensity and the cyst intensity, namely 15 dB. According to the analysis above, − 15 dB can just counteract the effect of sidelobe artefact.
For the speckle region, the signal power should stay unchanged. Usually, it is the same case with the mainlobedominated targets (e.g. bright points, hyperechoic regions). In some cases, increasing the weight for the mainlobedominated targets may separate the targets from the trailing artefact more clearly. As for the ultrasound image, an overall change of 3–5 dB is obvious. Given the above, 1.5 dB can distinguish the selected mainlobedominated regions from the surrounding sidelobe artifacts better without making the whole image darkened too much. In the meantime, the improvements in the contrast for the cysts using our method can also be preserved.
Algorithm routine
To summarize, we list the workflow of our proposed effective distancebased sidelobe reduction algorithm as below:
Algorithm 1 Algorithm for effective distancebased sidelobe reduction.
Input: The beamformed envelope value at a certain position, \(\varvec{X} = \left[ {x_{1} , \ldots ,x_{N} } \right] \in {\text{R}}^{1 \times N}\)
 Step 1.

Construct the sparse reconstruction coefficient matrix \(\varvec{P}\), and normalize each column of \(\varvec{P}\) to [0,1] using Eqs. (3)–(6)
 Step 2.

Compute the effective distance \(ED_{g}\) according to Eq. (7)
 Step 3.

Accomplish the target division using Eq. (9)
 Step 4.

Choose the targetdependent IFCF referring to Eq. (10)
 Step 5.

Weight the beamformed inphase/quadraturephase (IQ) data using the IFCF as Eq. (11) does.
Output: The interframe coherence weighted beamformed result at this position.
Then the steps above are repeated for all positions in a beamformed image. After the log compression, the output can then yield a Bmode image.
Simulation and phantom experiment setups
Experiments were devised to verify the effectiveness of our algorithm on the simulated and phantom experiment data. The data is obtained online from the challenge of the Plane wave Imaging in Medical UltraSound (PICMUS) unit of the 2016 IEEE International Ultrasonics Symposium (IUS) [27]. Originally there are 75 angles for each scene, which spread from − 16° to 16°. To verify the effectiveness of our proposed method with a limited frame number, we uniformly picked out 7 angles (− 16°, − 10.8°, − 5.6°, 0°, 5.6°, 10.8°, 16°) for our experiments. The parameters related to the sidelobe level, resolution and contrast were measured during the experiment.
Simulated study
The simulated data was acquired with the commonly used ultrasound simulation tool Field II [20]. In the Field II simulation, a 5.2 MHz, 128element linear array transducer was used. The sampling rate was set to 20.8 MHz. The excitation pulse was a twocycle sinusoid at the central frequency and the fractional bandwidth of the transducer was 60%.
There are two scenarios in the simulation, namely the PSF and the circular anechoic cysts in speckle. The former is used for the resolution test and the latter is for the contrast test. In these two simulation scenarios, five selected plane waves steer from − 4.3° to 4.3° at an interval of 1.7°. An attenuation coefficient of 0.5 dB/(MHz cm) has also been added in order to mimic the properties of the commercial phantom used for phantom experiments. The DAS beamformer is adopted for dynamic focus on the receiving end. No apodization is adopted.
Phantom experiment
The phantom data was acquired using a commercially calibrated generalpurpose multitissue phantom from CIRS (Model 040GSE, Computerized Imaging Reference Systems Inc., Norfolk, VA, USA), using a Verasonics research scanner (Verasonics Corporation, Kirkland, WA, USA) with channeldomain data acquisition capabilities. In the phantom study, a 5.2 MHz, 128element linear array transducer with a pitch of 0.3048 mm was used and the sampling frequency was 20.8 MHz. Also, the excitation pulse was a twocycle sinusoid at the central frequency and the fractional bandwidth of the transducer was 60%.
There are also two scenarios in the phantom experiments, namely the point targets region and the complex cysts region. In these two scenarios, five selected angles also spread from − 4.3° to 4.3° at an interval of 1.7°. The DAS beamformer is adopted for the dynamic focus on the receiving end. No apodization is adopted either.
Methods for comparison
For both the simulation and the phantom experiment, the algorithms at the receiving end are implemented in Matlab^{®}. Apart from the normal PWC and our proposed effective distancebased method, a SVD filter method [15] is also included in our experiment for comparison. This method is also designed for the PWC, and it performs well with more than 10 steering angles. In this method, the threshold \(\beta\) for the eigen vector number is set to 1 as the [15] does.
In the proposed method, the error tolerance \(\delta\) is set to 0.005 and the max iteration number is set to 200 in the sparse representation based solution. Usually, the solution procedure ends within three iterations. Other parameters are set as illustrated in “Parameters selection in our method” section.
Parameters for measurement
The quantitative tests are all done after the log compression.
Results
In this section, the results of three different beamforming schemes are shown for the comparison using the same plane wave dataset. Both simulation and phantom data are studied.
Simulated study
Point spread function (PSF)
FWHM and PSL for a PSF at z = 20.0 mm
Beamformer  FWHM (mm)  PSL (dB) 

Normal PWC  0.47  − 26.42 
SVD filter  0.48  − 36.62 
Our method  0.47  − 46.11 
Circular anechoic cysts in speckle
Contrast parameters of the simulated cyst lesions
Beamformer  CR (dB)  CNR 

Normal PWC  17.30  2.74 
SVD filter  20.75  3.00 
Our method  23.60  3.11 
Phantom experiment
Point targets region
FWHM and PSL for the point at z = 40.0 mm and contrast parameters in the phantom experiment
Beamformer  FWHM (mm)  PSL (dB)  CR (dB)  CNR 

Normal PWC  0.68  − 19.46  14.20  1.64 
SVD filter  0.68  − 24.22  15.27  1.79 
Our method  0.67  − 27.35  16.11  1.81 
Complex cysts region
Contrast parameters of the cyst lesion at z = 45 mm in the phantom
Beamformer  CR (dB)  CNR 

Normal PWC  20.43  2.66 
SVD filter  21.47  2.83 
Our method  23.62  3.07 
Experiments of number of angles
FWHM and PSL for a simulated PSF at z = 20.0 mm
Beamformer  FWHM (mm)  PSL (dB)  

3 angles  5 angles  7 angles  3 angles  5 angles  7 angles  
Normal PWC  0.47  0.47  0.47  − 20.52  − 26.42  − 31.70 
SVD filter  0.47  0.48  0.47  − 28.39  − 36.62  − 45.05 
Our method  0.47  0.47  0.46  − 36.41  − 46.11  − 52.65 
Experiments for noise robustness
Discussion
In this paper, we propose a novel sidelobe suppressing method based on the effective distance for the plane wave compounding with limited scanning times. The biggest innovation in our proposed method is that we introduce a novel global effective distance to measure the interframe coherence, which overcomes the difficulty of sidelobe localization in few frames. The whole process in the proposed method is quite like the image processing. The Step 1 and Step 2 correspond to the feature extraction in the signal domain. In the Step 3, we use the extracted feature to select the region of interest (ROI), namely the sidelobedominated area. Finally, we do the image enhancement to the specific ROI. It is worth noting that in the Step 2, we use the signal envelop value as the feature, different steering angles as the samples, and effective distance comparator as the classifier to do the region classification. This idea is ingenious.
As shown in [15], our last proposed method has a satisfactory side lobe suppressing performance when the steering angles are no less than 10. The new method aims to further reduce the number of frames required for compounding, thus we choose 7 angles for our experiments. Since the original angles spread from − 16° to 16° with the interval of 0.43°, we uniformly pick − 16°, − 10.8°, − 5.6°, 0°, 5.6°, 10.8°, 16° for our 7 angles. The angles still cover the range of − 16° to 16° with a larger interval. Besides, the uniform selection method can minimize the influence brought by the different intervals.
According to the results present in the last section, our method performs best in the sidelobe suppression and contrast enhancement under the limited frame number situation. In the meantime, the proposed coherence based method doesn’t affect the width of the PSF as the apodization method does. The reason is that our method is conducted on the envelope after DAS beamforming and has nothing to do with the original sampling signal. Thus the mainlobe width is preserved during our process. For comparison, we also conducted experiments using fewer angles (3 angles and 5 angles) with the results shown in 3.3. The results of all the experiments can embody the advantages of our method when we have few angles in the PWC. This indicates that our method may ensure a higher imaging time resolution. Finally, it is proved that the proposed method has high robustness against noise, which is one of its advantages to the MV. Consequently, the proposed method is believed to be a promising method to improve the ultrafast PWC image quality.
To summarize the computational complexity, the complexity of the MV beamformer is associated with the covariance matrix inversion. Because the dimension of the covariance matrix for subarray size L is L × L, its inverse needs operations of order O(L^{3}) using Gaussian elimination [30]. The main computational amount of the SVD filter method in [15] occurs on the SVD of the covariance matrix, which requires O(N^{3}) floating operations by using the Golub–Reinsch algorithm [31]. Our method constructs the bidirectional connectivity matrix \(\varvec{P}\) via the sparse representation using Eqs. (3)–(6), requiring O(N^{2}) operations given \(N\) frames. In brief, our method is the most computationally efficient among the three methods. As the graphics processing unit (GPU) acceleration is available for the implementation of ultrasound imaging nowadays [32], our approach is expected to be implemented in real time.
Although the results are good, there is still room for improvement in our method. We conclude it as the following points:
Firstly, the method of parameter selection in our method could be improved. In our proposed effective distance method, there are two sets of parameters to be tuned. The first set are the thresholds for the region division. The second set are the coherence weight factors for the different regions. The selection of the two sets of parameters is closely related to the imaging performance of the method. The current method of parameter selection is still empirical. The adaptive selection of the parameters is one of the efforts we should make.
Secondly, the only feature used in our sidelobe localization is the signal envelop intensity. Actually, the original channel signal contains more information. As the global effective distance can be used as a multifeatures classifier, the unused information, such as the phase information, harmonic component and attenuation coefficient etc., may also be included as the features in our localization. This may further improve the accuracy of the sidelobe location.
It is worth noting that, as a general similarity measure metric, the proposed effective distance method can also be used in other imaging modality with the compounding process, such as the synthetic aperture imaging and diverging wave imaging [33, 34]. Further research on the application of the method will also be included in our next phase of work.
Conclusions
This paper aims to settle the contradiction between the sidelobe suppression performance and the frame rate reservation in the ultrafast PWI. To this end, we put forward a novel global effective distance based sidelobe suppressing method for the PWC with a limited frame number. The effective distance is introduced to locate the sidelobeaffected region after the DAS beamforming. Then, a targetdependent coherence factor is employed to suppress the sidelobe in the compounding result. Simulation and experimental data were used to evaluate the performances of the different imaging methods. Results demonstrate that our proposed sidelobe reduction method can obtain better performance in terms of the sidelobe suppression and imaging contrast in comparison with the normal PWC and the SVD filter method. Meanwhile, the high resolution of the normal PWC is also retained. Considering these performances, we believe the proposed method could be a more promising approach in enhancing the ultrafast PWI imaging quality. Although our method shows certain potential in the existing experiments, the in vivo experiment is needed in the future.
It is worth noting that the new method can also be used in other imaging modalities using the compounding technique, which will be our future work.
Notes
Authors’ contributions
The authors declare equal contribution. All authors read and approved the final manuscript.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (61771143).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The dataset supporting the conclusions of this article is available on the IUS 2016 website, https://www.creatis.insalyon.fr/Challenge/IEEE_IUS_2016/download.
Consent for publication
Not applicable.
Ethics approval and consent to participate
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Publisher’s Note
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