Sub-Nyquist Sampling and Fourier Domain Beamforming in Volumetric Ultrasound Imaging

Enhancing single-element compressive ultrasound imaging through novel random aperture masking and data mixing strategy

As ultrasound techniques continue to evolve, the integration of compressed sensing technology has emerged as a pivotal advancement, offering a transformative impact on the landscape of ultrasound imaging. A key attribute of compressed sensing lies in its ability to facilitate a substantial reduction in both machinery size and power consumption. This technological synergy not only addresses crucial practical considerations in the design of ultrasound systems but also opens avenues for enhanced portability and energy efficiency. This study develops a model and introduces an aperture mask with a mixing scheme for compressive ultrasound imaging employing a single transducer, aiming to minimize the loss of information and scrutinize the variables influencing image quality while facilitating computationally efficient system simulation. A detailed procedural guide is presented for generating synthetic data, accompanied by qualitative and quantitative analyses using several sparse recovery methods under different experimental conditions. This study's analysis reveals that the proposed strategy achieves improved metrics, offering advantages for sparse recovery. Specifically, the finite element results demonstrate approximately a 10% improvement in the condition number of the measurement matrix, reflecting enhanced numerical stability.

Speed-enhanced scattering compensation method with sub-Nyquist sampling

A rapid feedback-based scattering compensation method is particularly important for guiding light precisely within turbid tissues, especially the dynamic tissues. However, the huge number of measurements that come from the underutilization of the signal frequency channel greatly limits the modulation speed. This paper introduces a rapid compensation method with the sub-Nyquist sampling which improves the channel utilization and the speed of wavefront shaping. The number of measurements is reduced to ∼1500 with 32 × 32 freedom, and the PBR of the focus reaches ∼200. The system performances are demonstrated by focusing the light through brain slices of different thicknesses.

High Frame Rate Ultrasound Imaging by Means of Tensor Completion: Application to Echocardiography

High frame rate ultrasound (US) imaging enables the monitoring of fast-moving organs. In echocardiography, this is especially needed due to the existence of rapidly moving structures, such as the heart valves. In the last two decades, various methods have been proposed to improve the frame rate. Here, we propose a novel method, based on binary coding patterns (BCPs) and tensor completion (TC), to increase the temporal resolution (i.e., frame rate) in the preprocessing stage of conventional focused ultrasound imaging (CFUI). The rationale behind our proposal is to perform, at first, the beamforming of a fraction of the scan lines, randomly selected in each frame based on BCP. Then, we reconstruct the missing scan lines through TC. The latter is an effective technique for recovering missing information from a low-rank tensor, based on a small number of observations using rank minimization. Following our approach, reducing the transmissions events needed to generate an image, the frame rate is increased by the same proportion. We have applied the proposed technique to a pre-beamformed radio frequency (RF) echocardiographic dataset. Our results show that we can improve the frame rate by a factor from 3 to 4, while keeping the structural similarity (SSIM) of the reconstructed tensor and the original one at values higher than 0.98.

Requirements and Hardware Limitations of High-Frame-Rate 3-D Ultrasound Imaging Systems

The spread of high frame rate and 3-D imaging techniques has raised pressing requirements for ultrasound systems. In particular, the processing power and data transfer rate requirements may be so demanding to hinder the real-time (RT) implementation of such techniques. This paper first analyzes the general requirements involved in RT ultrasound systems. Then, it identifies the main bottlenecks in the receiving section of a specific RT scanner, the ULA-OP 256, which is one of the most powerful available open scanners and may therefore be assumed as a reference. This case study has evidenced that the “star” topology, used to digitally interconnect the system’s boards, may easily saturate the data transfer bandwidth, thus impacting the achievable frame/volume rates in RT. The architecture of the digital scanner was exploited to tackle the bottlenecks by enabling a new “ring“ communication topology. Experimental 2-D and 3-D high-frame-rate imaging tests were conducted to evaluate the frame rates achievable with both interconnection modalities. It is shown that the ring topology enables up to 4400 frames/s and 510 volumes/s, with mean increments of +230% (up to +620%) compared to the star topology.

High-Frequency Ultrasound Imaging With Sub-Nyquist Sampling

Implementation of a high-frequency ultrasound (HFUS) beamformer is computationally challenging because of its high sampling rate. This article introduces an efficient beamformer with sub-Nyquist sampling (or bandpass sampling) that is suitable for HFUS imaging. Our approach used channel radio frequency data sampled at bandpass sampling rate (i.e., 4/ 3f_c ) and postfiltering-based interpolation to reduce the computational complexity. A polyphase structure for interpolation was used to further reduce the computational burden while maintaining an adequate delay resolution ( δ ). The performance of the proposed beamformer (i.e., 4/ 3f_c sampling with sixfold interpolation, δ = 8f_c ) was compared with that of the conventional method (i.e., 4f_c sampling with fourfold interpolation, δ = 16f_c ). Ultrafast coherent compounding imaging was used in simulation, in vitro and in vivo imaging experiments. Axial/lateral resolution and contrast-to-noise ratio (CNR) values were measured for quantitative evaluation. The number of transmit pulse cycles was varied from 1 to 3 using two transducers with different fractional bandwidths (67% and 98%). In the simulation, the proposed and conventional methods showed the similar -6-dB axial beam widths (63.5 and 61.5 μm , respectively) from the two-cycle transmit pulse using the transducer with a bandwidth of 67%. In vitro and in vivo imaging experiments were performed using a Verasonics ultrasound research platform equipped with a high-frequency array transducer (20-46 MHz). The in vitro imaging results using a wire target showed consistent results with the simulation study (i.e., disparity at -6-dB axial resolution). The in vivo feasibility study with a murine mouse model with breast cancer was also performed, and the proposed method yielded a similar image quality compared with the conventional method. From these studies, it was demonstrated that the proposed HFUS beamformer based on the bandpass sampling can substantially reduce the computational complexity while minimizing the loss of spatial resolution for HFUS imaging.

Switchable and Tunable Deep Beamformer Using Adaptive Instance Normalization for Medical Ultrasound

Recent proposals of deep learning-based beamformers for ultrasound imaging (US) have attracted significant attention as computational efficient alternatives to adaptive and compressive beamformers. Moreover, deep beamformers are versatile in that image post-processing algorithms can be readily combined. Unfortunately, with the existing technology, a large number of beamformers need to be trained and stored for different probes, organs, depth ranges, operating frequency, and desired target 'styles', demanding significant resources such as training data, etc. To address this problem, here we propose a switchable and tunable deep beamformer that can switch between various types of outputs such as DAS, MVBF, DMAS, GCF, etc., and also adjust noise removal levels at the inference phase, by using a simple switch or tunable nozzle. This novel mechanism is implemented through Adaptive Instance Normalization (AdaIN) layers, so that distinct outputs can be generated using a single generator by merely changing the AdaIN codes. Experimental results using B-mode focused ultrasound confirm the flexibility and efficacy of the proposed method for various applications.

Sparse Convolutional Beamforming for 3-D Ultrafast Ultrasound Imaging

Real-time 3-D ultrasound (US) provides a complete visualization of inner body organs and blood vasculature, crucial for diagnosis and treatment of diverse diseases. However, 3-D systems require massive hardware due to the huge number of transducer elements and consequent data size. This increases cost significantly and limit both frame rate and image quality, thus preventing the 3-D US from being common practice in clinics worldwide. A recent study presented a technique called sparse convolutional beamforming algorithm (SCOBA), which obtains improved image quality while allowing notable element reduction in the context of 2-D focused imaging. In this article, we build upon previous work and introduce a nonlinear beamformer for 3-D imaging, called COBA-3D, consisting of 2-D spatial convolution of the in-phase and quadrature received signals. The proposed technique considers diverging-wave transmission and achieves improved image resolution and contrast compared with standard delay-and-sum beamforming while enabling a high frame rate. Incorporating 2-D sparse arrays into our method creates SCOBA-3D: a sparse beamformer that offers significant element reduction and, thus, allows performing 3-D imaging with the resources typically available for 2-D setups. To create 2-D thinned arrays, we present a scalable and systematic way to design 2-D fractal sparse arrays. The proposed framework paves the way for affordable ultrafast US devices that perform high-quality 3-D imaging, as demonstrated using phantom and ex-vivo data.

Variational Formulation of Unsupervised Deep Learning for Ultrasound Image Artifact Removal

Recently, deep learning approaches have been successfully used for ultrasound (US) image artifact removal. However, paired high-quality images for supervised training are difficult to obtain in many practical situations. Inspired by the recent theory of unsupervised learning using optimal transport driven CycleGAN (OT-CycleGAN), here, we investigate the applicability of unsupervised deep learning for US artifact removal problems without matched reference data. Two types of OT-CycleGAN approaches are employed: one with the partial knowledge of the image degradation physics and the other with the lack of such knowledge. Various US artifact removal problems are then addressed using the two types of OT-CycleGAN. Experimental results for various unsupervised US artifact removal tasks confirmed that our unsupervised learning method delivers results comparable to supervised learning in many practical applications.

Current Development and Applications of Super-Resolution Ultrasound Imaging

Abnormal changes of the microvasculature are reported to be key evidence of the development of several critical diseases, including cancer, progressive kidney disease, and atherosclerotic plaque. Super-resolution ultrasound imaging is an emerging technology that can identify the microvasculature noninvasively, with unprecedented spatial resolution beyond the acoustic diffraction limit. Therefore, it is a promising approach for diagnosing and monitoring the development of diseases. In this review, we introduce current super-resolution ultrasound imaging approaches and their preclinical applications on different animals and disease models. Future directions and challenges to overcome for clinical translations are also discussed.

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.

Adaptive and Compressive Beamforming Using Deep Learning for Medical Ultrasound

In ultrasound (US) imaging, various types of adaptive beamforming techniques have been investigated to improve the resolution and the contrast-to-noise ratio of the delay and sum (DAS) beamformers. Unfortunately, the performance of these adaptive beamforming approaches degrades when the underlying model is not sufficiently accurate and the number of channels decreases. To address this problem, here, we propose a deep-learning-based beamformer to generate significantly improved images over widely varying measurement conditions and channel subsampling patterns. In particular, our deep neural network is designed to directly process full or subsampled radio frequency (RF) data acquired at various subsampling rates and detector configurations so that it can generate high-quality US images using a single beamformer. The origin of such input-dependent adaptivity is also theoretically analyzed. Experimental results using the B-mode focused US confirm the efficacy of the proposed methods.

Ultrasound Sub-pixel Motion-tracking Method with Out-of-plane Motion Detection for Precise Vascular Imaging

Ultrasound vascularity imaging provides important information for differential diagnosis of tumors. Peak-hold (PH) is a useful technique for precisely imaging small vessels by selecting a maximum brightness in each pixel through the frames obtained sequentially. To use PH successfully one needs motion compensation to reduce image blur, but out-of-plane motion cannot be avoided. To address this problem, we developed a sub-pixel motion-tracking method with out-of-plane motion detection (OPMD). It is a combination of the sum of the absolute differences (SAD) method and the Kanade-Lucas-Tomasi method and can be accurately applied to various motions. The value from OPMD (γ) is defined as a statistical value obtained from the distribution of residual values in the SAD procedure with the obtained frames. The value is ideally 0, and the frames having large γ are removed from the PH procedure. The accuracy of the proposed tracking method was found by a simulation study to be approximately 20 μm. We also found, through a phantom experiment, that the value of γ sensitively increased enough to detect out-of-plane motion. Most important, γ begins to increase before tracking errors occur. This suggests that OPMD can be used to predict tracking errors and effectively remove frames from the PH procedure. An in vivo experiment with a rabbit showed that the PH image obtained with motion tracking clearly revealed peripheral vessels that were blurred in the PH image obtained without motion tracking. We also found that the image quality becomes better when OPMD was used to remove frames including out-of-plane motion.

Fourier-Domain Beamforming and Structure-Based Reconstruction for Plane-Wave Imaging

Ultrafast imaging based on coherent plane-wave compounding is one of the most important recent developments in medical ultrasound. It significantly improves the image quality and allows for much faster image acquisition. This technique, however, requires large computational load motivating methods for sampling and processing rate reduction. In this work, we extend the recently proposed frequency-domain beamforming (FDBF) framework to plane-wave imaging. Beamforming in frequency yields the same image quality while using fewer samples. It achieves at least fourfold sampling and processing rate reduction by avoiding oversampling required by standard processing. To further reduce the rate, we exploit the structure of the beamformed signal and use compressed sensing methods to recover the beamformed signal from its partial frequency data obtained at a sub-Nyquist rate. Our approach obtains tenfold rate reduction compared with standard time-domain processing. We verify performance in terms of spatial resolution and contrast based on the scans of a tissue mimicking the phantom obtained by a commercial Aixplorer system. In addition, in vivo carotid and thyroid scans processed using standard beamforming and FDBF are presented for qualitative evaluation and visual comparison. Finally, we demonstrate the use of FDBF for shear-wave elastography by generating velocity maps from the beamformed data processed at sub-Nyquist rates.

High-Volume-Rate 3-D Ultrasound Imaging Based on Synthetic Aperture Sequential Beamforming With Chirp-Coded Excitation

Three-dimensional (3-D) ultrasound imaging is a promising modality for many medical applications. Unfortunately, it generates voluminous data in the front end, making it unattractive for high-volume-rate portable medical applications. We apply synthetic aperture sequential beamforming (SASB) to greatly compress the front-end receive data. Baseline 3-D SASB has a low volume rate, because subapertures fire one by one. In this paper, we propose to increase the volume rate of 3-D SASB without degrading imaging quality through: 1) transmitting and receiving simultaneously with four subapertures and 2) using linear chirps as the excitation waveform to reduce interference. We design four linear chirps that operate on two overlapped frequency bands with chirp pairs in each band having opposite chirp rates. Direct implementation of this firing scheme results in grating lobes. Therefore, we design a sparse array that mitigates the grating lobe levels through optimizing the locations of transducer elements in the bin-based random array. Compared with the baseline 3-D SASB, the proposed method increases the volume rate from 8.56 to 34.2 volumes/s without increasing the front-end computation requirement. Field-II-based cyst simulations show that the proposed method achieves imaging quality comparable with baseline 3-D SASB in both shallow and deep regions.

Ultrasonic Phased Array Compressive Imaging in Time and Frequency Domain: Simulation, Experimental Verification and Real Application

Embracing the fact that one can recover certain signals and images from far fewer measurements than traditional methods use, compressive sensing (CS) provides solutions to huge amounts of data collection in phased array-based material characterization. This article describes how a CS framework can be utilized to effectively compress ultrasonic phased array images in time and frequency domains. By projecting the image onto its Discrete Cosine transform domain, a novel scheme was implemented to verify the potentiality of CS for data reduction, as well as to explore its reconstruction accuracy. The results from CIVA simulations indicate that both time and frequency domain CS can accurately reconstruct array images using samples less than the minimum requirements of the Nyquist theorem. For experimental verification of three types of artificial flaws, although a considerable data reduction can be achieved with defects clearly preserved, it is currently impossible to break Nyquist limitation in the time domain. Fortunately, qualified recovery in the frequency domain makes it happen, meaning a real breakthrough for phased array image reconstruction. As a case study, the proposed CS procedure is applied to the inspection of an engine cylinder cavity containing different pit defects and the results show that orthogonal matching pursuit (OMP)-based CS guarantees the performance for real application.

CColor and Vector Flow Imaging in Parallel Ultrasound with Sub-Nyquist Sampling

RF acquisition with a high-performance multi-chan-nel ultrasound system generates massive datasets in short periods of time, especially in "ultrafast" ultrasound when digital receive beamforming is required. Sampling at a rate four times the carrier frequency is the standard procedure since this rule complies with the Nyquist-Shannon sampling theorem and simplifies quadrature sampling. Bandpass sampling (or undersampling) outputs a band-pass signal at a rate lower than the maximal frequency without harmful aliasing. Advantages over Nyquist sampling are reduced storage volumes and data workflow, and simplified digital signal processing tasks. We used RF undersampling in color flow imag-ing (CFI) and vector flow imaging (VFI) to decrease data volume significantly (factor of 3 to 13 in our configurations). CFI and VFI with Nyquist and sub-Nyquist samplings were compared in vitro and in vivo. The estimate errors due to undersampling were small or marginal, which illustrates that Doppler and vector Doppler im-ages can be correctly computed with a drastically reduced amount of RF samples. Undersampling can be a method of choice in CFI and VFI to avoid information overload and reduce data transfer and storage.

Ultrasound Imaging From Sparse RF Samples Using System Point Spread Functions

Upcoming phased-array 2-D sensors will soon enable fast high-definition 3-D ultrasound imaging. Currently, the communication of raw radio-frequency (RF) channel data from the probe to the computer for digital beamforming is a bottleneck. For reducing the amount of transferred data samples, this paper investigates the design of an adapted sparse sampling technique for image reconstruction inspired by the compressed sensing framework. Echo responses from isolated points are generated using a physically based simulation of ultrasound wave propagation through tissues. These point spread functions form a dictionary of shift-variant bent waves, which depend on the specific sound excitation and acquisition protocols. Speckled ultrasound images can be approximately decomposed in this dictionary where sparsity is enforced at the system matrix design. The Moore-Penrose pseudoinverse is precomputed and used at the reconstruction stage for fast minimum-norm recovery from nonuniform pseudorandom sampled raw RF data. Results on simulated and acquired phantoms demonstrate the benefits of an optimized basis function design for high-quality B-mode image recovery from few RF channel data samples.

FoCUS: Fourier-Based Coded Ultrasound

Modern imaging systems typically use single-carrier short pulses for transducer excitation. Coded signals together with pulse compression are successfully used in radar and communication to increase the amount of transmitted energy. Previous research verified significant improvement in signal-to-noise ratio (SNR) and imaging depth for ultrasound imaging with coded signals. Since pulse compression needs to be applied at each transducer element, the implementation of coded excitation (CE) in array imaging is computationally complex. Applying pulse compression on the beamformer output reduces the computational load but degrades both the axial and lateral point spread function, compromising image quality. In this paper, we present an approach for efficient implementation of pulse compression by integrating it into frequency domain beamforming. This method leads to significant reduction in the amount of computations without affecting axial resolution. The lateral resolution is dictated by the factor of savings in computational load. We verify the performance of our method on a Verasonics imaging system and compare the resulting images to time-domain processing. The computational savings are evaluated for a minimal sampling rate of four times the central frequency. We show that from 4- to 33-fold reduction is achieved as a function of the resulting lateral resolution, with no degradation of axial resolution. For an imaging system operating at a higher sampling rate, e.g., 10 times the central frequency, the savings can be as high as 77-fold. The efficient implementation makes CE a feasible approach in array imaging with the potential to enhance SNR as well as improve imaging depth and frame rate.