Extension of Fourier-Based Techniques for Ultrafast Imaging in Ultrasound With Diverging Waves

Advanced Fourier migration for Plane-Wave vector flow imaging

Ultrafast ultrasound imaging modalities have been studied extensively in the ultrasound community. It breaks the compromise between the frame rate and the region of interest by imaging the whole medium with wide unfocused waves. Continuously available data allow monitoring fast transient dynamics at hundreds to thousands of frames per second. This feature enables a more accurate and robust velocity estimation in vector flow imaging (VFI). On the other hand, the huge amount of data and real-time processing demands are still challenging in VFI. A solution is to provide a more efficient beamforming approach with smaller computation complexity than the conventional time-domain beamformer like delay-and-sum (DAS). Fourier-domain beamformers are shown to be more computationally efficient and can provide equally good image quality as DAS. However, previous studies generally focus on B-mode imaging. In this study, we propose a new framework for VFI which is based on two advanced Fourier migration methods, namely, slant stack migration (SSM) and ultrasound Fourier slice beamform (UFSB). By carefully modifying the beamforming parameters, we successfully apply the cross-beam technique within the Fourier beamformers. The proposed Fourier-based VFI is validated in simulation studies, in vitro, and in vivo experiments. The velocity estimation is evaluated via bias and standard deviation and the results are compared with conventional time-domain VFI using the DAS beamformer. In the simulation, the bias is 6.4%, -6.2%, and 5.7%, and the standard deviation is 4.3%, 2.4%, and 3.9% for DAS, UFSB, and SSM, respectively. In vitro studies reveal a bias of 4.5%, -5.3%, and 4.3% and a standard deviation of 3.5%, 1.3%, and 1.6% from DAS, UFSB, and SSM, respectively. The in vivo imaging of the basilic vein and femoral bifurcation also generate similar results using all three methods. With the proposed Fourier beamformers, the computation time can be shortened by up to 9 times and 14 times using UFSB and SSM.

Fourier Beamformation for Convex-Array Diverging Wave Imaging Using Virtual Sources

Convex probes have been widely used in clinical abdominal imaging for providing deep penetration and wide field of view. Ultrafast imaging modalities have been studied extensively in the ultrasound community. Specifically, broader wavefronts, such as plane wave and spherical wave, are used for transmission. For convex array, spherical wavefront can be simply synthesized by turning all elements simultaneously. Due to the lack to transmit focus, the image quality is suboptimal. One solution is to adopt virtual sources behind the transducer and compound corresponding images. In this work, we propose two novel Fourier-domain beamformers (vs1 and vs2) for nonsteered diverging wave imaging and an explicit interpolation scheme for virtual-source-based steered diverging wave imaging using a convex probe. The received echoes are first beamformed using the proposed beamformers and then interpolated along the range axis. A total of 31 virtual sources located on a circular line are used. The lateral resolution, the contrast ( C ), and the contrast-to-noise ratio (CNR) are evaluated in simulations, phantom experiments, ex vivo imaging of the bovine heart, and in vivo imaging of the liver. The results show that the two proposed Fourier-domain beamformers give higher contrast than dynamic receive focusing (DRF) with better resolution. In vitro results demonstrate the enhancement on CNR: 6.7-dB improvement by vs1 and 5.9-dB improvement by vs2. Ex vivo imaging experiments on the bovine heart validate the CNR enhancements by 8.4 dB (vs1) and 8.3 dB (vs2). In vivo imaging on the human liver also reveals 6.7- and 5.5-dB improvements of CNR by vs1 and vs2, respectively. The computation time of vs1 and vs2, depending on the image pixel number, is shortened by 2-73 and 4-216 times than the DRF.

Complex Convolutional Neural Networks for Ultrafast Ultrasound Imaging Reconstruction From In-Phase/Quadrature Signal

Ultrafast ultrasound imaging remains an active area of interest in the ultrasound community due to its ultrahigh frame rates. Recently, a wide variety of studies based on deep learning have sought to improve ultrafast ultrasound imaging. Most of these approaches have been performed on radio frequency (RF) signals. However, in- phase/quadrature (I/Q) digital beamformers are now widely used as low-cost strategies. In this work, we used complex convolutional neural networks for reconstruction of ultrasound images from I/Q signals. We recently described a convolutional neural network architecture called ID-Net, which exploited an inception layer designed for reconstruction of RF diverging-wave ultrasound images. In the present study, we derive the complex equivalent of this network, i.e., complex-valued inception for diverging-wave network (CID-Net) that operates on I/Q data. We provide experimental evidence that CID-Net provides the same image quality as that obtained from RF-trained convolutional neural networks, i.e., using only three I/Q images, CID-Net produces high-quality images that can compete with those obtained by coherently compounding 31 RF images. Moreover, we show that CID-Net outperforms the straightforward architecture that consists of processing real and imaginary parts of the I/Q signal separately, which thereby indicates the importance of consistently processing the I/Q signals using a network that exploits the complex nature of such signals.

In Vivo Evaluation of Plane Wave Imaging for Abdominal Ultrasonography

Although plane wave imaging (PWI) has been extensively employed for ultrafast ultrasound imaging, its potential for sectorial B-mode imaging with a convex array transducer has not yet been widely recognized. Recently, we reported an optimized PWI approach for sector scanning that exploits the dynamic transmit focusing capability. In this paper, we first report the clinical applicability of the optimized PWI for abdominal ultrasonography by in vivo image and video evaluations and compare it with conventional focusing (CF) and diverging wave imaging (DWI), which is another dynamic transmit focusing technique generally used for sectorial imaging. In vivo images and videos of the liver, kidney, and gallbladder were obtained from 30 healthy volunteers using PWI, DWI, and CF. Three radiologists assessed the phantom images, 156 in vivo images, and 66 in vivo videos. PWI showed significantly enhanced (p < 0.05) spatial resolution, contrast, and noise and artifact reduction, and a 4-fold higher acquisition rate compared to CF and provided similar performances compared to DWI. Because the computations required for PWI are considerably lower than that for DWI, PWI may represent a promising technique for sectorial imaging in abdominal ultrasonography that provides better image quality and eliminates the need for focal depth adjustment.

Compressed Sensing Approach for Reducing the Number of Receive Elements in Synthetic Transmit Aperture Imaging

Recently, researchers have shown an increased interest in ultrasound imaging methods alternate to conventional focused beamforming (CFB). One such approach is based on the synthetic aperture (SA) scheme; more popular are the ones based on synthetic transmit aperture (STA) schemes with a single-element transmit or multielement STA (MSTA). However, one of the main challenges in translating such methods to low-cost ultrasound systems is the tradeoffs among image quality, frame rate, and complexity of the system. These schemes use all the transducer elements during receive, which dictates a corresponding number of parallel receive channels, thus increasing the complexity of the system. A considerable amount of literature has been published on compressed sensing (CS) for SA imaging. Such studies are aimed at reducing the number of transmissions in SA but still recover images of acceptable quality at high frame rate and fail to address the complexity due to full-aperture receive. In this work, we adopt a CS framework to MSTA, with a motivation to reduce the number of receive elements and data. The CS recovery performance was assessed for the simulation data, tissue-mimicking phantom data, and an example in vivo biceps data. It was found that in spite of using 50% receive elements and overall using only 12.5% of the data, the images recovered using CS were comparable to those of reference full-aperture case in terms of estimated lateral resolution, contrast-to-noise ratio, and structural similarity indices. Thus, the proposed CS framework provides some fresh insights into translating the MSTA imaging method to affordable ultrasound scanners.

Temporal Super-resolution of Ultrasound Imaging Using Matrix Completion

The temporal super-resolution of the dynamic ultrasound imaging, a means to observe rapid heart movements, is considered an important subject in medical diagnosis of cardiac conditions. Here, a new technique based on the acquisition scheme using the matrix completion (MC) theory is offered for the temporal super-resolution of the two-dimensional (2D) and three-dimensional (3D) ultrasound imaging. MC mentions the problem of completing a low-rank matrix when only a subset of its elements can be observed. Here, the lower scan lines are acquired. Whereby, the proposed method uses temporal and spatial information of the radio frequency (RF) image sequences for the reconstruction of skipped RF lines. This is performed using the construction of the MC images and then reconstruction of them by the MC theory. The results of the proposed method are compared with the compressive sensing (CS) reconstruction methods. The qualitative and quantitative evaluations of 2D and 3D data demonstrate that in the proposed method, which uses the spatial and temporal relation of RF images and the MC theory, the reconstruction is more accurate, and the reconstruction error is lower. The computational complexity of this method is very low. It also does not require hardware adjustments. Therefore, it can be easily implemented in current ultrasound-imaging devices with the frame-rate enhancement. For instance, the frame rate up to two times the original sequence is feasible using the proposed methods, while root mean square error is decreased by about 35% and 30% for 2D and 3D data, respectively, compared with the CS reconstruction method.

Strategic Undersampling and Recovery Using Compressed Sensing for Enhancing Ultrasound Image Quality

In conventional focused beamforming (CFB), there is a known tradeoff between the active aperture size of the ultrasound transducer array and the resulting image quality. Increasing the size of the active aperture leads to an increase in the image quality of the ultrasound system at the expense of increased system cost. An alternate approach is to get rid of the requirement of having consecutive active receive elements and instead place them in a random order in a larger aperture. This, in turn, creates an undersampled situation where there are only M active elements placed in a larger aperture, which can accommodate N consecutive receive elements (with ). It is possible to formulate and solve the above-mentioned undersampling situation using a compressed sensing (CS) approach. In our previous work, we had proposed Gaussian undersampling strategy for reducing the number of active receive elements. In this work, we introduce a novel framework, namely Gaussian undersampling-based CS framework (GAUCS) with wave atoms as a sparsifying basis for CFB imaging method. The performance of the proposed method is validated using simulation and in vitro phantom data. Without an increase in the active elements, it is found that the proposed GAUCS framework improved the lateral resolution (LR) and image contrast by 27% and 1.5 times, respectively, while using 16 active elements and by 39% and 1.1 times, respectively, while using 32 active elements. Thus, the GAUCS framework can play a significant role in improving the performance, especially, of affordable point-of-care ultrasound systems.

Comparison Between Multiline Transmission and Diverging Wave Imaging: Assessment of Image Quality and Motion Estimation Accuracy

High frame rate imaging is particularly important in echocardiography for better assessment of the cardiac function. Several studies showed that diverging wave imaging (DWI) and multiline transmission (MLT) are promising methods for achieving a high temporal resolution. The aim of this study was to compare MLT and compounded motion compensation (MoCo) DWI for the same transmitted power, same frame rates [image quality and speckle tracking echocardiography (STE) assessment], and same packet size [tissue Doppler imaging (TDI) assessment]. Our results on static images showed that MLT outperforms DW in terms of resolution (by 30% on average). However, in terms of contrast, MLT outperforms DW only for the depth of 11 cm (by 40% on average), the result being reversed at a depth of 4 cm (by 27% on average). In vitro results on a spinning phantom at nine different velocities showed that similar STE axial errors (up to 2.3% difference in median errors and up to 2.1% difference in the interquartile ranges) are obtained with both ultrafast methods. On the other hand, the median lateral STE estimates were up to 13% more accurate with DW than with MLT. On the contrary, the accuracy of TDI was only up to ~3% better with MLT, but the achievable DW Doppler frame rate was up to 20 times higher. However, our overall results showed that the choice of one method relative to the other is therefore dependent on the application. More precisely, in terms of image quality, DW is more suitable for imaging structures at low depths, while MLT can provide an improved image quality at the focal point that can be placed at higher depths. In terms of motion estimation, DW is more suitable for color Doppler-related applications, while MLT could be used to estimate velocities along selected lines of the image.

Wide Field-of-View Ultrafast Curved Array Imaging Using Diverging Waves

Ultrafast ultrasound imaging provides great opportunities for very high frame rate applications, such as shear wave elastography and microvascular imaging. However, ultrafast imaging with curved array transducers remains challenging in terms of element directivity and a limited field-of-view (FOV) for a fully synthetic area. In this paper, a wide FOV ultrafast curved array imaging method based on diverging wave transmissions is presented for high frame rate abdominal ultrasound applications. For this method, a theoretical model for a diverging wave solution based on a virtual point source originating from a circular line is proposed, and the FOV and element directivity are analyzed by this model. Furthermore, an integrated model for plane wave and diverging wave imaging along the location of the virtual point source is derived. The proposed method was evaluated with simulation, phantom, and in vivo studies. In the simulation and phantom studies, the image quality (i.e., spatial resolution, cystic resolution, and contrast-to-noise ratio), and effective FOV were assessed. For the in vivo study, a preliminary result from abdominal microvascular imaging, where diverging wave excitation was utilized to depict the vasculature, was also presented. In the renal cortex microvessels, the diverging wave imaging yielded a higher signal-to-clutter ratio value than the plane wave imaging, i.e., 6.35 vs. 4.26 dB, due to the wider synthetic field. These studies demonstrated that the proposed ultrafast curved array imaging technique based on diverging wave excitation allowed for an extended FOV with high spatiotemporal resolution.

Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging

Recently, compressed sensing (CS) has been applied to ultrasound imaging for either data reduction or frame rate improvement. However, there are no detailed reports yet on strategies for lateral undersampling of channel data in conventional focused beamforming (CFB) and its recovery exploiting the CS approach. We propose a strategic lateral undersampling approach for channel data using the Gaussian sampling scheme and compare it with a direct extension of the often-used uniform undersampling reported for axial undersampling to the lateral direction and 2-D random sampling reported in the literature. As opposed to the reported 2-D random undersampling, we explore undersampling of channel data in the lateral direction by acquiring radiofrequency data from only a reduced number of chosen receive elements and subjecting these data to further undersampling in the axial direction. The effect of the sampling schemes on CS recovery was studied using data from simulations and experiments for various lateral and axial undersampling rates. The results suggest that CS-recovered data from the Gaussian distribution-based channel data subsampling yielded better recovery and contrast in comparison to those obtained from the often-used uniform distribution-based undersampling. Although 90% of the samples from the original data using the proposed sampling scheme were discarded, the contrast of the CS-recovered image was comparable to that of the reference image. Thus, CS with the proposed Gaussian sampling scheme for channel data subsampling not only reduces the data size significantly, but also strategically uses only a few active receive elements in the process; thus, it can provide an attractive option for the affordable point-of-care ultrasound system.

Compressed Ultrasound Signal Reconstruction Using a Low-Rank and Joint-Sparse Representation Model

With the introduction of very dense sensor arrays in ultrasound (US) imaging, data transfer rate and data storage can become a bottleneck in US system design. To reduce the amount of sampled channel data, we propose a new approach based on the low-rank and joint-sparse model that allows us to exploit the correlations between different US channels and transmissions. With this method, the minimum number of measurements at each channel can be lower than the sparsity in compressive sensing theory. The accuracy of the reconstruction is less dependent on the sparse basis. An optimization algorithm based on the simultaneous direction method of multipliers is proposed to efficiently solve the resulting optimization problem. Results on different data sets with different experimental settings show that the proposed method is better adapted to the US signals and can recover the image with fewer samples (e.g., 10% of the samples) than the existing compressive sensing-based methods, while maintaining reasonable image quality.

Ultrasonic sector imaging using plane wave synthetic focusing with a convex array transducer

Synthetic transmit focusing (STF) methods using unfocused waves or plane waves (PWs) have recently been investigated extensively. However, STF using PWs with a convex array (PWSTF-CA) has not been rigorously studied for high-resolution sector imaging. In this paper, the authors suggest an analytical model for accurate characterization of the spatial beam patterns of PWSTF-CA using a large range of either uniformly or non-uniformly distributed PW angles. On the basis of the model, a frame-based PWSTF-CA approach with non-uniform PW angles is suggested to achieve superior image quality at a higher frame rate than conventional transmit focusing (CTF). The analytical model can also be used for optimal selection of a set of PW angles to scan the entire sectorial field of view and its subsets employed for STF at each imaging point. The authors also investigate how to select transmit subarrays for each of the PWs to obtain the best spatial resolution. A theoretical analysis and simulations are conducted for the verification of the analytical model and the optimal utilization strategy of PWSTF-CA. The results indicate that the PWSTF-CA improves not only the frame rate but also the contrast, signal-to-noise ratio, and resolution compared with the CTF, as in the case of PWSTF with linear arrays.

Experimental 3-D Ultrasound Imaging with 2-D Sparse Arrays using Focused and Diverging Waves

Three dimensional ultrasound (3-D US) imaging methods based on 2-D array probes are increasingly investigated. However, the experimental test of new 3-D US approaches is contrasted by the need of controlling very large numbers of probe elements. Although this problem may be overcome by the use of 2-D sparse arrays, just a few experimental results have so far corroborated the validity of this approach. In this paper, we experimentally compare the performance of a fully wired 1024-element (32 × 32) array, assumed as reference, to that of a 256-element random and of an “optimized” 2-D sparse array, in both focused and compounded diverging wave (DW) transmission modes. The experimental results in 3-D focused mode show that the resolution and contrast produced by the optimized sparse array are close to those of the full array while using 25% of elements. Furthermore, the experimental results in 3-D DW mode and 3-D focused mode are also compared for the first time and they show that both the contrast and the resolution performance are higher when using the 3-D DW at volume rates up to 90/second which represent a 36x speed up factor compared to the focused mode.

Ultrafast Ultrasound Imaging Using Combined Transmissions With Cross-Coherence-Based Reconstruction

Plane-wave-based ultrafast imaging has become the prevalent technique for non-conventional ultrasound imaging. The image quality, especially in terms of the suppression of artifacts, is generally compromised by reducing the number of transmissions for a higher frame rate. We hereby propose a new ultrafast imaging framework that reduces not only the side lobe artifacts but also the axial lobe artifacts using combined transmissions with a new coherence-based factor. The results from simulations, in vitro wire phantoms, the ex vivo porcine artery, and the in vivo porcine heart show that our proposed methodology greatly reduced the axial lobe artifact by 25±5 dB compared with coherent plane-wave compounding (CPWC), which was considered as the ultrafast imaging standard, and suppressed side lobe artifacts by 15 ± 5 dB compared with CPWC and coherent spherical-wave compounding. The reduction of artifacts in our proposed ultrafast imaging framework led to a better boundary delineation of soft tissues than CPWC.

High-Quality Plane Wave Compounding Using Convolutional Neural Networks

Single plane wave (PW) imaging produces ultrasound images of poor quality at high frame rates (ultrafast). High-quality PW imaging usually relies on the coherent compounding of several successive steered emissions (typically more than ten), which in turn results in a decreased frame rate. We propose a new strategy to reduce the number of emitted PWs by learning a compounding operation from data, i.e., by training a convolutional neural network to reconstruct high-quality images using a small number of transmissions. We present experimental evidence that this approach is promising, as we were able to produce high-quality images from only three PWs, competing in terms of contrast ratio and lateral resolution with the standard compounding of 31 PWs ( 10× speedup factor).