Fourier Domain Depth Migration for Plane-Wave Ultrasound Imaging

Fourier-based beamforming for 3D plane wave imaging and application in vector flow imaging using selective compounding

Objective. Ultrafast ultrasound imaging using planar or diverging waves for transmission is a promising approach for efficient 3D imaging with matrix arrays. This technique has advantages for B-mode imaging and advanced techniques, such as 3D vector flow imaging (VFI). The computation load of the cross-beam technique is associated with the number of transmit anglesmand receive anglesn. The full velocity vector is obtained using the least square fashion. However, the beamforming is repeatedm × ntimes using a conventional time-domain delay-and-sum (DAS) beamformer. In the 3D case, the collection and processing of data from different beams increase the amount of data that must be processed, requiring more storage capacity and processing power. Furthermore, the large computation complexity of DAS is another major concern. These challenges translate into longer computational times, increased complexity in data processing, and difficulty in real-time applications.Approach. In response to this issue, this study proposes a novel Fourier domain beamformer for 3D plane wave imaging, which significantly increases the computational speed. Additionally, a selective compounding strategy is proposed for VFI, which reduces the beamforming process fromm × ntom(wheremandnrepresent the number of transmission and reception, respectively), effectively shortening the processing time. The underlying principle is to decompose the receive wavefront into a series of plane waves with different slant angles. Each slant angle can produce a sub-volume for coherent or selective compounding. This method does not rely on the assumption that the plane wave is perfect and the results show that our proposed beamformer is better than DAS in terms of resolution and image contrast. In the case of velocity estimation, for the Fourier-based method, only Tx angles are assigned in the beamformer and the selective compounding method produces the final image with a specialized Rx angle.Main results. Simulation studies andin vitroexperiments confirm the efficacy of this new method. The proposed beamformer shows improved resolution and contrast performance compared to the DAS beamformer for B-mode imaging, with a suppressed sidelobe level. Furthermore, the proposed technique outperforms the conventional DAS method, as evidenced by lower mean bias and standard deviation in velocity estimation for VFI. Notably, the computation time has been shortened by 40 times, thus promoting the real-time application of this technique. The efficacy of this new method is verified through simulation studies andin vitroexperiments and evaluated by mean bias and standard deviation. Thein vitroresults reveal a better velocity estimation: the mean bias is 2.3%, 3.4%, and 5.0% forvx,vy, andvz, respectively. The mean standard deviation is 1.8%, 1.7%, and 3.4%. With DAS, the evaluated mean bias is 9.8%, 4.6%, and 6.7% and the measured mean standard deviation is 7.5%, 2.5%, and 3.9%.Significance. In this work, we propose a novel Fourier-based method for both B-mode imaging and functional VFI. The new beamformer is shown to produce better image quality and improved velocity estimation. Moreover, the new VFI computation time is reduced by 40 times compared to conventional methods. This new method may pave a new way for real-time 3D VFI applications.

Deconvolution based on sparsity and continuity improves the quality of ultrasound image

The application of ultrasound (US) image has been limited by its limited resolution, inherent speckle noise, and the impact of clutter and artifacts, especially in the miniaturized devices with restricted hardware conditions. In order to solve these problems, many researchers have explored a number of hardware modifications as well as algorithmic improvements, but further improvements in resolution, signal-to-noise ratio (SNR) and contrast are still needed. In this paper, a deconvolution algorithm based on sparsity and continuity (DBSC) is proposed to obtain the higher resolution, SNR, and, contrast. The algorithm begins with a relatively bold Wiener filtering for initial enhancement of image resolution in preprocessing, but it also introduces ringing noise and compromises the SNR. In further processing, the noise is suppressed based on the characteristic that the adjacent pixels of the US image are continuous as long as Nyquist sampling criterion is met, and the extraction of high-frequency information is balanced by using relatively sparse. Subsequently, the theory and experiments demonstrate that relative sparsity and continuity are general properties of US images. DBSC is compared with other deconvolution strategies through simulations and experiments, and US imaging under different transmission channels is also investigated. The final results show that the proposed method can greatly improve the resolution, as well as provide significant advantages in terms of contrast and SNR, and is also feasible in applications to devices with limited hardware.

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.

Improved Coherent Plane-Wave Compounding Using Sign Coherence Factor Weighting for Frequency-Domain Beamforming

This study proposes a novel modified sign coherence factor (SCF) weighting adapted to the frequency-domain (FD) beamforming for ultrasound plane-wave imaging to achieve a high frame rate and better image quality. First, before beamforming, the sign components were extracted from the radiofrequency signals of aperture data. Second, the modified SCF was established using the FD beamformed sign components. Finally, the FD beamformed image was weighted by the modified SCF. To assess the performance of the proposed modified SCF for FD beamforming, the resolution, contrast, computation complexity and execution time of the generated images were evaluated. The results revealed that the FD-SCF could significantly improve the computational load compared with the classic delay-and-sum SCF on the premise of equal image quality improvement. Therefore, high image quality and low computational load have been successfully combined under the proposed weighting method.

Circular statistics vector for improving coherent plane wave compounding image in Fourier domain

In this work, a circular statistics vector (CSV) weighting Fourier domain (FD) beamforming for ultrasound plane-wave images was proposed to achieve better image quality with a high frame rate. Firstly, the cosine and sine components of the instantaneous phase are extracted from undelayed RF signals. Secondly, the FD beamformed cosine and sine components are used to establish the CSV. Finally, the FD beamformed amplitude image is weighted by the CSV. The resolution, contrast, and computation complexity were used to assess the performance of the proposed method. The results revealed that FD_CSV could significantly reduce the computational load compared to the conventional DAS_CSV on the equal improvement of image quality. Besides, compared to coherence factor (CF), phase coherence factor (PCF), etc., based on variance calculation, the CSV based on mean resultant vector calculation can effectively preserve the speckle due to the more tolerant to phase errors. The proposed FD_CSV weighting method has successfully conducted high image quality and low computational load.

Inverse Problem of Ultrasound Beamforming With Denoising-Based Regularized Solutions

During the past few years, inverse problem formulations of ultrasound beamforming have attracted growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a regularization term that enforces a certain class on the resulting image. Here, we take advantage of alternating direction method of multipliers to propose a flexible framework in which each term is optimized separately. Furthermore, the proposed beamforming formulation is extended to replace the regularization term with a denoising algorithm, based on the recent approaches called plug-and-play (PnP) and regularization by denoising (RED). Such regularizations are shown in this work to better preserve speckle texture, an important feature in ultrasound imaging, than sparsity-based approaches previously proposed in the literature. The efficiency of the proposed methods is evaluated on simulations, real phantoms, and in vivo data available from a plane-wave imaging challenge in medical ultrasound. Furthermore, a comprehensive comparison with existing ultrasound beamforming methods is also provided. These results show that the RED algorithm gives the best image quality in terms of contrast index while preserving the speckle statistics.

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.

3-D ultrasonic image reconstruction in frequency domain using a virtual transducer model

In ultrasonic non-destructive testing, image reconstruction is essential to restore the diffracted ultrasound signals to improve the lateral resolution of images. Some reconstruction methods, like DAS-based synthetic aperture imaging, are inefficient, especially for reconstructing three-dimensional (3-D) images. Other methods do not provide high-resolution results, because they neglect the distortion effect introduced by transducer geometry. To overcome these disadvantages, we propose a 3-D ultrasonic image reconstruction method based on synthetic aperture wavenumber algorithm. It considers wave diffraction and transducer geometry effects, and can refocus the reflectors even in non-focal zone, which suits for large depth range imaging. This method builds a virtual transducer model in frequency domain by treating the focused transducer as a virtual planar transducer on its focal plane. In addition, the method uses non-uniform fast Fourier transform and deconvolution operation to achieve the 3-D image reconstruction, which has remarkably improved the efficiency and accuracy. According to the experimental results, the lateral resolution of an image reconstructed by the proposed method can reach 290.2 μm, exceeding the lateral resolution limitation of the 15 MHz focused transducer (523.24 μm). Furthermore, the proposed method only takes 0.744 s to reconstruct a 3-D image with 1000×100×100 pixels, while the time domain SAFT takes about 1163.8 s. It shows the potential for real-time 3-D imaging under advanced hardware.

Slant-Stack Migration Applied to Plane-Wave Ultrasound Imaging

Ultrafast plane-wave ultrasound imaging replaces numerous focused-beam transmissions with a single emitted plane-wave pulse, insonifying the entire subsurface region of interest all at once. To improve image quality, one can employ coherent plane wave compounding (CPWC), whereby several pulses are emitted sequentially at different steering angles, and their corresponding acquired raw data frames are individually beamformed and then combined to form a final reconstructed image frame. We describe a classic geophysical reconstruction technique called slant-stack migration, adapted here to CPWC imaging. Our evaluation results, based on two public-domain datasets featuring both anechoic and hyperechoic targets, demonstrate that the presented approach compares favorably with conventional delay-and-sum beamforming.

Phase-Shift Depth Migration for Plane-Wave Ultrasound Imaging

Plane-wave ultrasound imaging is an important modality that enables very high frame rates, which is necessary for adequate characterization of blood flow and tissue motion properties. This work describes a novel Fourier-domain method for plane-wave ultrasound image reconstruction that can be used in situations where the speed of sound varies with depth in a layered propagation medium. Our approach is based on geophysical phase-shift migration technique that has been modified to handle plane-wave ultrasound data processing. Our simulation results show that the proposed method is capable of accurately imaging point targets in a three-layer medium, mimicking tissue-bone-tissue ultrasound propagation.