Delay-and-sum Research Articles

Learning to sound imaging by a model-based interpretable network

Acoustic beamforming methods based on microphone arrays have been widely used for sound source localization in various industrial fields. The conventional methods such as Delay and Sum (DAS) beamforming are limited by poor spatial resolution although their computational complexity is low. Efforts have been made to improve the resolution of the beamforming map, achieved by both model-based and deep network-based approaches. However, the model-based methods usually suffer from high additional computational effort and largely rely on selecting user-determined parameters. The deep network-based methods may make it difficult to guarantee generalization as well as hard to generate the beamforming map directly. In this paper, we first propose a scheme DAMAS-FISTA-LASSO to solve the inverse problem of sound imaging, significantly reducing runtime requirements. By deep unfolding the proposed algorithm, we further have designed an end-to-end interpretable model-based deep neural network termed DAMAS-FISTA-LASSO-Net (DFLNet) for real-time and high-resolution mapping of acoustic sources, which could obtain satisfying performance on both simulated and real-world data, demonstrating the strong generalization capability of the network.

Ultrafast plane wave imaging of breast lesions

Ultrafast plane wave imaging has great potential for 3-D functional ultrasound imaging but also comes with decreased lateral resolution, contrast, and penetration depth with respect to conventional imaging (CI). By utilizing coherent plane-wave compound imaging (CPWCI) and different beam forming techniques (Delay and Sum (DAS), Stolt’s-fk, and Lu’s-fk), we have demonstrated to improve resolution, penetration, and contrast-to-noise ratio. In this work we evaluate this technique in patients. A Siemens Sequoia system equipped with an 18L6HD, 14L5, and 10L4 was used to acquire CI and CPWCI data in 77 patients suspected of breast cancer visiting our clinic. CI data was acquired at three angles (-11, 0, and 11 degrees) and beamformed in the Sequoia and incoherently compounded while CPWCI data was acquired for 33 angles (-16:1:16 degrees) and subsequently processed off-line. In total, 9 malignant lesions, 35 benign lesions, and 32 normal other structures were found. For all three transducers, improved penetration was observed with CPWCI compared to CI. Additionally, contrast to noise ratio was also improved by CPWCI, especially at larger imaging depths. Qualitatively, an improved resolution appeared to be present, probably also caused by the improved contrast. Currently, a reader study in which radiologists have to score CI and CPWCI images sight by side while blinded to the acquisition mode is being prepared to test the efficacy of CPWCI in clinical practice. In conclusion, CPWCI bears great promise for improved breast cancer detection.

Microwave Angiography by Ultra-Wideband Sounding: A Preliminary Investigation.

Angiography is a very informative method for physicians such as cardiologists, neurologists and neuroscientists. The current modalities experience some shortages, e.g., ultrasound is very operator dependent. The computerized tomography (CT) and magnetic resonance (MR) angiography are very expensive and near infrared spectroscopy cannot capture the deep arteries. Microwave technology has the potential to address some of these issues while compromising between operator dependency, cost, speed, penetration depth and resolution. This paper studies the feasibility of microwave signals for monitoring of arteries. To this aim, a homogenous phantom mimicking body tissue is built. Four elastic tubes simulate arteries and a mechanical system creates pulsations in these arteries. A multiple input multiple output (MIMO) array of ultra-wideband (UWB) transmitters and receivers illuminates the phantom and captures the reflected signals over the desired observation time period. Since we are only interested in the imaging of dynamic parts, i.e., arteries, the static clutters can be suppressed easily by background subtraction method. To obtain a fast image of arteries, which are pulsating with the heartbeat rate, we calculate the Fourier transform of each channel of the MIMO system over the observation time and apply delay and sum (DAS) beamforming method on the heartbeat rate aligned spectral component. The results show that the lateral and longitudinal images and motion mode (M-mode) time series of different points of phantom have the potential to be used for diagnosis.

F-number optimization for synthetic aperture delay-multiply-and-sum reconstruction

The choices of transmit and receive f-numbers impact both ultrasound image contrast and spatial resolution. Although previous studies have evaluated the impact of receive f-number in delay-and-sum (DAS) plane wave imaging, there has not been a systematic study of f-numbers in DAS or delay-multiply-and-sum (DMAS) synthetic aperture (SA) imaging. In this study, we measured the impact on main lobe to side lobe energy ratio (MSER), generalized contrast-to-noise ratio (gCNR), and spatial resolution when varying receive and transmit f-numbers from 1 to 5 in 0.2 increments in DAS and DMAS reconstructed SA images. A wire target in a water tank and a standard imaging phantom were used to measure these metrics. From the water tank wire target images, higher MSER values were achieved with middle-range transmit f-numbers (2–4) and high receive f-numbers (>4) for both DAS and DMAS. From the phantom contrast target images, DAS produced images with high gCNR when using high transmit f-numbers (>4) and high receive f-numbers (>4). This came at the cost of reduced spatial resolution. DMAS produced images with high gCNR when using low transmit f-numbers (<3) and high receive f-numbers (>4). DMAS was not found to have as severe of a tradeoff in spatial resolution when seeking maximum gCNR. However, gCNR was typically lower for DMAS than DAS. For both DAS and DMAS, point target images had high spatial resolution when using low receive f-numbers (<2). Spatial resolution was typically higher for DMAS than DAS. Hanning apodization was found to produce similar trends as those found with rectangular apodization. These findings give insight on the behaviors of DAS and DMAS SA reconstruction algorithms and could be used to guide f-number selection.

Fast 3D Super-Resolution Ultrasound With Adaptive Weight-Based Beamforming.

Super-resolution ultrasound (SRUS) imaging through localising and tracking sparse microbubbles has been shown to reveal microvascular structure and flow beyond the wave diffraction limit. Most SRUS studies use standard delay and sum (DAS) beamforming, where high side lobes and broad main lobes make isolation and localisation of densely distributed bubbles challenging, particularly in 3D due to the typically small aperture of matrix array probes. This study aimed to improve 3D SRUS by implementing a new fast 3D coherence beamformer based on channel signal variance. Two additional fast coherence beamformers, that have been implemented in 2D were implemented in 3D for the first time as comparison: a nonlinear beamformer with p-th root compression and a coherence factor beamformer. The 3D coherence beamformers, together with DAS, were compared in computer simulation, on a microflow phantom and in vivo. Simulation results demonstrated that all three adaptive weight-based beamformers can narrow the main lobe, suppress the side lobes, while maintaining the weaker scatter signals. Improved 3D SRUS images of microflow phantom and a rabbit kidney within a 3-second acquisition were obtained using the adaptive weight-based beamformers, when compared with DAS. The adaptive weight-based 3D beamformers can improve the SRUS and the proposed variance-based beamformer performs best in simulations and experiments. Fast 3D SRUS would significantly enhance the potential utility of this emerging imaging modality in a broad range of biomedical applications.

Improved Ultrafast Power Doppler Imaging Using United Spatial-Angular Adaptive Scaling Wiener Postfilter.

Ultrafast power Doppler imaging (uPDI) using high-frame-rate plane-wave transmission is a new microvascular imaging modality that offers high Doppler sensitivity. However, due to the unfocused transmission of plane waves, the echo signal is subject to interference from noise and clutter, resulting in a low signal-to-noise ratio (SNR) and poor image quality. Adaptive beamforming techniques are effective in suppressing noise and clutter for improved image quality. In this study, an adaptive beamformer based on a united spatial-angular adaptive scaling Wiener (uSA-ASW) postfilter is proposed to improve the resolution and contrast of uPDI. In the proposed method, the signal power and noise power of the Wiener postfilter are estimated by uniting spatial and angular signals, and a united generalized coherence factor (uGCF) is introduced to dynamically adjust the noise power estimation and enhance the robustness of the method. Simulation and in vivo data were used to verify the effectiveness of the proposed method. The results show that the uSA-ASW can achieve higher resolution and significant improvements in image contrast and background noise suppression compared with conventional delay-and-sum (DAS), coherence factor (CF), spatial-angular CF (SACF), and adaptive scaling Wiener (ASW) postfilter methods. In the simulations, uSA-ASW improves contrast-to-noise ratio (CNR) by 34.7 dB (117.3%) compared with DAS, while reducing background noise power (BNP) by 52 dB (221.4%). The uSA-ASW method provides full-width at half-maximum (FWHM) reductions of [Formula: see text] (59.5%) and [Formula: see text] (56.9%), CNR improvements of 25.6 dB (199.9%) and 42 dB (253%), and BNP reductions of 46.1 dB (319.3%) and 12.9 dB (289.1%) over DAS in the experiments of contrast-free human neonatal brain and contrast-free human liver, respectively. In the contrast-free experiments, uSA-ASW effectively balances the performance of noise and clutter suppression and enhanced microvascular visualization. Overall, the proposed method has the potential to become a reliable microvascular imaging technique for aiding in more accurate diagnosis and detection of vascular-related diseases in clinical contexts.

Benefits of software beamforming for ultrasonic inspections

Nondestructive testing (NDT) is used in more and more industries and inspection techniques must constantly adapt to complex materials (coarse grained materials, composites, etc.), defects (corrosion, fatigue crack, HTHA, etc.) or new inspection standards. Ultrasonic imaging methods have long been limited by low data throughput and a small number of transducers, but this is no longer the case with nowadays electronic devices and computers which enable large amounts of raw data to be acquired and processed in real time. The Delay-and-Sum (DAS) algorithm, which has been used almost automatically in many applications over the past few years, is now outperformed by advanced processing methods. In this context, this article presents few real-time advanced reconstruction techniques that enhance the quality of ultrasonic images on typical industrial applications. The first example concerns coherence beamformers such as Phase Coherence Imaging (PCI) which exploit the phase information of the signals. This type of method proves to be highly effective in detecting diffraction echoes from crack-like defects or in improving contrast and resolution of images from corroded samples inspections. The second example uses cross-correlation techniques that have been known for years to improve detection in various fields. Correlating the data with the transmitted signal reduces electronic noise and improves signal-to-noise ratio. This application also benefits from recent progress of ultrasonic devices that are able to modulate complex excitation signals in emission. This type of method is very promising for the inspection of attenuative materials and coarse-grained steels.

Efficient Sigma-Delta Sensor Array Beamforming.

Nowadays, sensors with built-in sigma-delta modulators (ΣΔMs) are widely used in consumer, industrial, automotive, and medical applications, as they have become a cost-effective and convenient way to deliver data to digital processors. This is the case for micro-electro-mechanical system (MEMS), digital microphones that convert analog audio to a pulse-density modulated (PDM) bitstream. However, as the ΣΔMs output a PDM signal, sensors require either built-in or external high-order decimation filters to demodulate the PDM signal to a baseband multi-bit pulse-code modulated (PCM) signal. Because of this extra circuit requirement, the implementation of sensor array algorithms, such as beamforming in embedded systems (where the processing resources are critical) or in very large-scale integration (VLSI) circuits (where the power and area are crucial) becomes especially expensive as a large number of parallel decimation filters are required. This article proposes a novel architecture for beamforming algorithm implementation that fuses delay and decimation operations based on maximally flat (MAXFLAT) filters to make array processing more affordable. As proof of concept, we present an implementation example of a delay-and-sum (DAS) beamformer at given spatial and frequency requirements using this novel approach. Under these specifications, the proposed architecture requires 52% lower storage resources and 19% lower computational resources than the most efficient state-of-the-art architecture.

Full Waveform Inversion for NDT using ultrasonic linear arrays

Ultrasonic (UT) imaging is a widespread technique for nondestructive testing (NDT). The state-of-the-art UT image reconstruction algorithms are based on delay-and-sum (DAS) operations, which assume constant acoustic velocity across the tested objects and also neglects nonlinear effects such as diffractions and multiple reflections. These assumptions limit the reconstruction capabilities of DAS-based algorithms, especially for complex objects composed by several materials. In seismology, Full Waveform Inversion (FWI) methods have been used to obtain subsurface properties based on scattered and transmitted sound waves - which is a very similar problem to ultrasonic imaging in NDT - using the full wave information, showing promising results. In this paper, we present the application of FWI in NDT using simulated data representing acquisitions with a common linear array transducer. We review the theoretical formulation of FWI and discuss some difficulties that arise when it is applied to NDT. Image reconstruction is performed using both a state-of-the-art DAS algorithm, namely the Total Focusing Method, and FWI. The implementation targets a GPU platform, using the CUDA API. This leverages the highly parallelizable nature of the simulations and the FWI algorithm. The obtained results show that FWI can show more internal structures than TFM, with less information about the specimen. To foster further development, all source codes are provided.

Constraint matrix projection minimum variance beamformer based on adaptive decomposition threshold for ultrasound imaging

The eigenspace-based minimum variance (ESBMV) beamformer can enhance the contrast of the minimum variance (MV), but the traditional orthogonal projection and fixed eigen-decomposition threshold make it difficult to obtain further improvement in resolution and speckle uniformity. In this paper, a constraint matrix projection minimum variance based on adaptive decomposition threshold (ADCPMV) is proposed for ultrasound imaging, which aims to improve the insufficiency of ESBMV. Firstly, a constraint matrix with direction information is put forward to better remove the interference and noise of MV weight. Then, a threshold decomposition function based on truncated smoothed coherence factor (TSF) is proposed to eliminate dark-area artifacts. Finally, the TSF is used as the weighting to improve the ADCPMV contrast. Simulations and the experimental datasets of ats_wires, geabr_0 and rat_tumor are introduced to inspect the performance of the proposed algorithms. The result of point target simulation shows that the full-width at half-maximum (FWHM) of ADCPMV-TSF is reduced by 93.98% and 80.19% than that of traditional delay-and-sum (DAS) and ESBMV respectively. Furthermore, the geabr_0 experimental result shows that compared with traditional DAS and ESBMV, the FWHM of ADCPMV-TSF is improved by 87.74% and 61.19% respectively. Meanwhile, the proposed ADCPMV-TSF can well avoid the generation of dark-area artifacts and get the maximal improvement of speckle signal-to-noise ratio is 103.57%.

Decorrelated compounding of synthetic aperture ultrasound imaging to detect low contrast thermal lesions induced by focused ultrasound

PurposeDecorrelated Compounding (DC) for synthetic aperture ultrasound can reduce speckle variation in images, suggesting enhanced detectability of low-contrast targets in tissue including thermal lesions produced by focused ultrasound (FUS). The DC imaging method has primarily been investigated in simulation and in phantom studies. This work investigates the feasibility of the DC method in monitoring thermal therapy via image guidance and non-invasive thermometry based on the change in backscattered energy (CBE). MethodsEx vivo porcine tissue was exposed to FUS exposures at acoustic powers of 5 W and 1 W, with peak pressure amplitudes of 0.64 MPa and 0.27 MPa respectively. During FUS exposure, RF echo data frames was acquired using a 7.8 MHz linear array probe and a Verasonics VantageTM ultrasound scanner (Verasonics Inc., Redmond, WA). RF echo data was taken to produce B-mode images, as reference images. Synthetic aperture RF echo data was also acquired and processed using delay-and-sum (DAS), a combination of spatial and frequency compounding referred to as Traditional Compounding (TC), and the proposed DC imaging methods. Image quality was assessed using the contrast-to-noise ratio (CNR) at the FUS beam focus, and the speckle SNR (sSNR) of the background region as preliminary metrics. A calibrated thermocouple was placed near the FUS beam focus for temperature measurements and calibrations using the CBE method. ResultsThe DC imaging method significantly improved image quality to detect low contrast thermal lesions in treated ex vivo porcine tissue in comparison to other imaging methods. In comparison to B-mode imaging, the lesion CNR measured using the DC imaging was shown to improve up to a factor of approximately 5.5. The corresponding sSNR improved by a factor of approximately 4.2 in comparison to B-mode imaging. CBE calculation using the DC imaging method yielded more precise measurements of the backscattered energy compared to other imaging methods studied. ConclusionsThe despeckling performance of the DC imaging method significantly improves the lesion CNR in comparison to B-mode imaging. This suggests that the proposed method can detect low-contrast thermal lesions induced by FUS therapy that are not detectable using standard B-mode imaging. Furthermore, the signal change at the focal point were more precisely measured by DC imaging, and the signal change in response to FUS exposure follows the temperature profile more closely than changes measured using B-mode, as well as synthetic aperture DAS and TC images. These suggest that DC imaging can potentially be used with the CBE method to improve non-invasive thermometry.

Multibeam minimum variance beamforming for ring array ultrasound imaging

Objective. Delay-and-sum (DAS) and minimum variance (MV) are two of the most important beamformers researched in ultrasound imaging. Compared with DAS, MV beamformer is different in respect of the aperture weights calculation, and can enhance the image quality by minimizing interference signal power. Various MV beamformers in linear array are studied, but linear array only provides a limited field of view. Ring array can provide better resolution and a full viewing angle; however, few studies have been explored based on ring array transducers. Approach. In this study, we proposed the multibeam MV (MB-MV) beamformer based on the conventional MV to enhance the image quality in ring array ultrasound imaging. To assess the effectiveness of the proposed approach, we conducted simulations, phantom experiments, and in vivo human experiments to compare MB-MV with DAS and spatial smoothing (SS) MV beamformers. Main results. The results show that the MB-MV method achieves at least 50% enhancement in terms of full width at half maximum compared to the others. Additionally, the MB-MV method improves the contrast ratio by approximate 6 dB and 4 dB compared with DAS and SS MV, respectively. Significance. This work demonstrates the feasibility of MB-MV method for ring array ultrasound imaging, and proves that MB-MV can improve the imaging quality in medical ultrasound imaging. According to our results, MB-MV method provides great potential in distinguishing between lesion and non-lesion areas in clinics, and further promotes the practical application of ring arrays in ultrasound imaging.

Improving Visualization of Osteochondritis Dissecans Using Delay-Multiply-and-Sum Reconstruction

Osteochondritis dissecans (OCD) of the capitellum is a joint defect that is common among adolescent athletes. It is important to diagnose OCD as early as possible, because early-stage OCD lesions have a high rate of spontaneous healing with rest. Medical ultrasound could potentially be used as a screening tool for OCD but is limited by the use of delay-and-sum (DAS) reconstruction. In this study, we tested conventional delay-multiply-and-sum (DMAS) and novel low-pass DMAS reconstruction algorithms for better visualization of OCD lesions. We created phantom and cadaveric OCD models that simulated a range of OCD lesion severities and stabilities. We also imaged an in vivo case of OCD in a patient study. In the reconstructed images, several profiles were taken to measure OCD lesion contrast, cartilage contrast, crack thickness error and bone interface clarity. In the phantom and cadaveric OCD models, we found that histogram-matched conventional DMAS reconstruction improved lesion contrast by up to 16%, cartilage contrast by 26% and bone interface clarity by 15% on average compared with DAS reconstruction. Histogram-matched low-pass DMAS reconstruction improved lesion contrast by up to 22%, cartilage contrast by 45%, and bone interface clarity by 29% on average compared with DAS reconstruction. In the in vivo case of OCD, we found that histogram-matched conventional and low-pass DMAS reconstruction improved lesion contrast by 22% and 26%, respectively. The application of DMAS reconstruction improved the ability of medical ultrasound to detect OCD lesions of the capitellum when compared with DAS reconstruction.

Beamspace-domain learning of minimum variance beamformer with fully convolutional network

In medical ultrasound systems, receiving beamforming is necessary to produce an ultrasonic image. Although minimum variance (MV) beamforming was developed to achieve higher image quality than commonly used delay-and-sum (DAS) beamforming, it is computationally expensive. Therefore, in this study, we investigated how to convert the beamforming profile of DAS to that of MV using deep learning. The results showed that a fully convolutional network could produce an image with comparable quality to that in MV beamforming in a shorter time than the conventional MV beamformer.

Fast Beamforming Method for Plane Wave Compounding Based on Beamspace Adaptive Beamformer and Delay-Multiply-and-Sum.

Although the use of coherent plane wave compounding is a promising technique for enabling the attainment of very high frame rate imaging, it achieves relatively low image quality because of data-independent reconstruction. Adaptive beamformers rather than delay-and-sum (DAS) conventional techniques have been proposed to improve the imaging quality. The minimum variance (MV) and delay-multiply-and-sum (DMAS) beamformers have been validated as effective in improving image quality. The MV improves mainly the resolution of the image, while being computationally expensive and having little impact on contrast. The DMAS increases the contrast while over-suppressing the speckle region in the case of 2-D summation for multi-transmission applications. In a new approach, a beamformer based on MV and DMAS is proposed to enhance both spatial resolution and contrast in plane wave imaging. Prior to estimating the weight vector of MV, the backscattered echoes are decorrelated without any spatial smoothing. This enhances the robustness of MV without compromising the improvement in resolution. With a shift from element space to beamspace, MV weights are calculated using the spatial statistics of a set of orthogonal beams, which allows the high-complexity algorithm to be run faster. After that, the MV weights are applied to the DMAS output vector beamformed over different transmissions. The proposed method can result in better contrast resolution, thereby avoiding over-suppression. The complexity of the applied DMAS version is also similar to that of DAS. Imaging results reveal that the proposed method offers improvements over the traditional compounding method in terms of spatial and contrast resolution. It also can achieve a higher image quality compared with some existing adaptive methods applied in the literature.

A Double Fourier-Transform Imaging Algorithm for a 24 GHz FMCW Short-Range Radar.

A frequency-modulated continuous-wave radar for short-range target imaging, assembling a transceiver, a PLL, an SP4T switch, and a serial patch antenna array, was realized. A new algorithm based on a double Fourier transform (2D-FT) was developed and compared with the delay and sum (DAS) and multiple signal classification (MUSIC) algorithms proposed in the literature for target detection. The three reconstruction algorithms were applied to simulated canonical cases evidencing radar resolutions close to the theoretical ones. The proposed 2D-FT algorithm exhibits an angle of view greater than 25° and is five times faster than DAS and 20 times faster than the MUSIC one. The realized radar shows a range resolution of 55 cm and an angular resolution of 14° and is able to correctly identify the positions of single and multiple targets in realistic scenarios, with errors lower than 20 cm.

Implementation and Comparison of Three Image Reconstruction Algorithms in FPGA Toward Palm-Size Photoacoustic Tomography

Photoacoustic (PA) imaging has been widely applied in both preclinical and clinical applications. With a significantly increasing number of data acquisition channels, fast high-quality image reconstruction with low-cost for PA imaging is an open challenge. In this paper, we propose a palm-size PAT system, named palmPAT, to achieve miniaturized low-cost PA imaging modality with high performance. To prove the feasibility, Field Programmable Gate Array (FPGA) implementation of PA image reconstruction is performed to achieve high-quality imaging performance with miniaturized size and cost. This FPGA implementation can be easily adapted to widely used algorithms, such as delay-and-sum (DAS) and its variants (e.g. DMAS, DAS-CF). We have performed in-vivo human finger experiments to demonstrate the feasibility and potential. To our best knowledge, this is the first study concentrated on the implementation and comparison of three frequently-used PA image reconstruction algorithms based on FPGA platform.

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.

Dynamic Speed of Sound Adaptive Transmission-Reflection Ultrasound Computed Tomography.

Ultrasound computed tomography (USCT) can visualize a target with multiple imaging contrasts, which were demonstrated individually previously. Here, to improve the imaging quality, the dynamic speed of sound (SoS) map derived from the transmission USCT will be adapted for the correction of the acoustic speed variation in the reflection USCT. The variable SoS map was firstly restored via the optimized simultaneous algebraic reconstruction technique with the time of flights selected from the transmitted ultrasonic signals. Then, the multi-stencils fast marching method was used to calculate the delay time from each element to the grids in the imaging field of view. Finally, the delay time in conventional constant-speed-assumed delay and sum (DAS) beamforming would be replaced by the practical computed delay time to achieve higher delay accuracy in the reflection USCT. The results from the numerical, phantom, and in vivo experiments show that our approach enables multi-modality imaging, accurate target localization, and precise boundary detection with the full-view fast imaging performance. The proposed method and its implementation are of great value for accurate, fast, and multi-modality USCT imaging, particularly suitable for highly acoustic heterogeneous medium.

Differential constant-beamwidth beamforming with cube arrays

In this paper, we present an azimuth and elevation constant-beamwidth (CB) differential beamforming approach for cube arrays. We decompose a global cube beamformer into a Kronecker-product (KP) of three sub-beamformers: two constant-beamwidth beamformers along the y and z axes, and a tunable super-directive (SD) beamformer along the x-axis. We propose two design methods to derive cube beamformers whose either white noise gain (WNG) or directivity factor (DF) may be set by design. We show that the CB threshold frequency with respect to the azimuth and elevation angles, and the WNG and DF performance, can be controlled by the number of microphones along each axis. In addition, we focus on the particular case of merely a single microphone along the x-axis, which yields a rectangular azimuth and elevation CB beamformer. We demonstrate that its CB threshold frequencies are controlled by the number of microphones along the y and z axes, and show that the WNG and DF performance measures are maximized when the two axes are equal in size. Finally, we analyze the performance of the proposed beamformers through simulations of speech signals in various reverberant scenarios, including deviations in the desired speech signal’s direction of arrival (DOA). We show that the proposed beamformers outperform previously-presented beamformers and the traditional SD and delay-and-sum (DS) beamformers, particularly in terms of the intelligibility of their corresponding time-domain enhanced signals.