Nonlinear Beamforming Research Articles

High-Resolution Power Doppler Using Null Subtraction Imaging.

To improve the spatial resolution of power Doppler (PD) imaging, we explored null subtraction imaging (NSI) as an alternative beamforming technique to delay-and-sum (DAS). NSI is a nonlinear beamforming approach that uses three different apodizations on receive and incoherently sums the beamformed envelopes. NSI uses a null in the beam pattern to improve the lateral resolution, which we apply here for improving PD spatial resolution both with and without contrast microbubbles. In this study, we used NSI with three types of singular value decomposition (SVD)-based clutter filters and noise equalization to generate high-resolution PD images. An element sensitivity correction scheme was also proposed as a crucial component of NSI-based PD imaging. First, a microbubble trace experiment was performed to evaluate the resolution improvement of NSI-based PD over traditional DAS-based PD. Then, both contrast-enhanced and contrast free ultrasound PD images were generated from the scan of a rat brain. The cross-sectional profile of the microbubble traces and microvessels were plotted. FWHM was also estimated to provide a quantitative metric. Furthermore, iso-frequency curves were calculated to provide a resolution evaluation metric over the global field of view. Up to six-fold resolution improvement was demonstrated by the FWHM estimate and four-fold resolution improvement was demonstrated by the iso-frequency curve from the NSI-based PD microvessel images compared to microvessel images generated by traditional DAS-based beamforming. A resolvability of [Formula: see text] was measured from the NSI-based PD microvessel image. The computational cost of NSI-based PD was only increased by 40 percent over the DAS-based PD.

An efficiency-improved GPU algorithm for the 2 + 2 + 1 method in nonlinear beamforming

Abstract Nonlinear beamforming (NLBF) has emerged as a highly effective technology for enhancing seismic data quality. The crux of NLBF's success lies in its ability to robustly estimate local traveltime operators directly from input data, a process that entails solving millions or even billions of nonlinear optimization problems per input gather. Among the solvers utilized for estimating these operators is the 2 + 2 + 1 method, for which we have previously introduced algorithmic implementations on both the CPU and GPU platforms. In this paper, we present an efficiency-improved GPU algorithm for the 2 + 2 + 1 method, particularly beneficial when dealing with small data apertures in NLBF. Our enhanced GPU algorithm brings significant improvements in computation efficiency through several strategic measures, which include leveraging Horner's method to minimize the mathematical overhead of traveltime calculation, implementing a GPU-friendly data reduction algorithm to exploit GPU computational power, and optimizing shared GPU memory usage as the primary workspace whenever feasible. To demonstrate the tangible efficiency enhancement achieved by our new GPU algorithm, via two illustrative examples, we compare its performance with that of our previous implementation.

Contrast-free microvessel imaging using null subtraction imaging combined with harmonic imaging

Ultrasound localization microscopy (ULM) has superior spatial resolution; however, it requires contrast agents and long data acquisition and processing time. Null subtraction imaging (NSI) is a nonlinear beamforming technique that improves the spatial resolution and reduces grating lobes with low computational cost. We combined pulse-inversion (PI) nonlinear imaging with NSI to increase resolution. Pulses with center frequency of 10.42 MHz and its inverted version were transmitted to obtain the second harmonic at 20.84 MHz (wavelength of ∼74 μm). The transducer pitch was 35% larger than the wavelength of the receive signal, which would introduce grating lobes in the field of view. A total of 1000, 9-angle (−8 to 8 degree in 2 degrees step) coherently compounded frames were acquired in 1 s. SVD filters were applied in raw RF data to filter out tissue signal. The dc offset was set to 0.1 in NSI imaging. Grating lobes, which were obvious in DAS images, were removed in the NSI images. Higher spatial resolution and contrast were observed from the NSI microvessel images. The spatial resolution of the NSI images using harmonic imaging approached one fourth of a wavelength with computation time increased by only 40% compared to DAS.

Nonlinear beamforming for intracardiac echocardiography: a comparative study.

The online version contains supplementary material available at 10.1007/s13534-024-00352-9.

A COMPARISON OF COHERENCE FACTOR AND SIGN COHERENCE FACTOR APPLIED TO A NONLINEAR BEAMFORMER

A new nonlinear beamformer named Double-Stage Delay Multiply and Sum (DS-DMAS) has recently been proposed as a variant of the Delay Multiply and Sum (DMAS) algorithm. DS-DMAS expands DMAS into a summation of multiple terms and considers this summation as Delay and Sum (DAS). In order to address the shortage of DAS, DS-DMAS replaced the DAS with DMAS. However, the construction of the new signal in the DS-DMAS algorithm still employs the DAS method. While DAS is a well-established and reliable method, its output is solely dependent on the signal amplitude. Therefore, signal similarity-based methods such as the Coherence Factor (CF) and the Sign Coherence Factor (SCF) have been proposed to weigh the DAS output and optimize its performance. Taking this into consideration, we incorporated the CF and SCF to weigh each newly generated signal in DS-DMAS, resulting in the Coherence Factor-based Double-Stage Delay Multiply and Sum (DS-DMAS-CF) and the Sign Coherence Factor-based Double-Stage Delay Multiply and Sum (DS-DMAS-SCF) approaches. Our focus is primarily on comparing the performance of DS-DMAS-CF and DS-DMAS-SCF. The results indicate that DS-DMAS-SCF exhibits better noise suppression capabilities compared to DS-DMAS-CF.

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.

Detection of microcalcifications using nonlinear beamforming techniques.

Abundant research demonstrates that early detection of cancer leads to improved patient prognoses. By detecting cancer earlier, when tumors are in their primary stages, treatment can be applied before metastases have occurred. The presence of microcalcifications (MCs) is indicative of malignancy in the breast, i.e., 30-50% of all nonpalpable breast cancers detected using mammograms are based on identifying the presence of MCs. Therefore, improving the ability to detect MCs with modern imaging technology remains an important goal. Specifically, improving the sensitivity of ultrasound imaging techniques to detect MCs in the breast will provide an important role for the early detection and diagnosis of breast cancer. In this work, a novel nonlinear beamforming technology for ultrasonic arrays is investigated for its ability to detect MCs. The beamforming technique, called null subtraction imaging (NSI), utilizes nulls in the beam pattern to create images using ultrasound. NSI provides improved lateral resolution, a reduction in side lobes, and an accentuation of bright singular targets. Therefore, it was hypothesized that the use of NSI would result in identification of more MCs in rat tumors having a speckle background. To test this hypothesis, rats with tumors were injected with Hydroxyapatite (HA) particles to mimic MCs. Ultrasound was used to scan the rat tumors and images were constructed using conventional delay and sum and using NSI beamforming. Three readers with experience in diagnostic ultrasound imaging examined the 1,344 images and scored the presence or absence of MCs. In all, 336 different tumor image slices were recorded and each reconstructed using NSI or conventional delay and sum with Hann apodization. In every image where one or MCs were detected in the Hann reconstructions, MCs were detected in the NSI images. In nine rat tumor images, one or more MCs were detected in the NSI images but not in the Hann images. Statistically, the results did support the hypothesis that NSI would increase the number of MCs detected in the rat tumors.

A joint method of coherence factor and nonlinear beamforming for synthetic aperture imaging with a ring array.

Ultrasound computed tomography (USCT) with a ring array is an emerging diagnostic method for breast cancer. In the literature, synthetic aperture (SA) imaging has employed the delay-and-sum (DAS) beamforming technique for ring-array USCT to obtain isotropic resolution reflection images. However, the images obtained by the conventional DAS beamformer suffer from off-axis clutter and low resolution due to inhomogeneity of the medium and phase distortion. To address these issues, researchers have developed adaptive beamforming methods, such as coherence factor (CF) and convolutional beamforming algorithm (COBA), that improve image quality. In this study, we propose a joint method that combines CF with short-lag COBA (SLCOBA). First, we estimate the average sound speed using CF to address tissue inhomogeneity. Based on the corrected sound speed map, SLCOBA effectively suppresses side lobes and enhances image quality. Numerical results show that the proposed method reduces clutter and noise, improving resolution performance. These findings suggest that the proposed method may be a practical option for breast imaging in inhomogeneous mediums in the future.

Beam multiply and sum: A tradeoff between delay and sum and filtered delay multiply and sum beamforming for ultrafast ultrasound imaging

The delay and sum (DAS) has been the popular beamforming algorithm for image reconstruction in ultrafast ultrasound imaging systems due to its low complexity implementation. However, to improve the lower contrast and resolution in images reconstructed using DAS, there have been many adaptive and non-linear beamforming algorithms developed in the recent past. One of the popular non-linear algorithms proposed in the literature, filtered delay multiply and sum (F-DMAS) is sensitive to off-axis clutters and produces artifacts that result in the degradation of the overall image quality along with a possible dynamic range alteration. In this work, a novel approach to combining the strengths of DAS and F-DMAS algorithms is proposed. The proposed approach referred to as beam multiply and sum (BMAS), employs a DAS beamformer in multiple sub-apertures at receive to form the sub-aperture beams and cross multiplies them using a multiply and sum architecture to enhance the spatial coherence and suppress the clutter artifacts. An exhaustive performance comparison in terms of dynamic range alteration, resolution, and contrast of the BMAS is performed with standard in-silico and in-vitro datasets. The results suggest that the proposed approach outperforms the DAS and F-DMAS beamformers in most cases. More than the proposal of a novel beamforming algorithm, to the best of our knowledge, the approach is the first attempt of its kind towards the possibility of the co-existence of two or more beamformers in an ultrasound imaging system. With optimal tuning, it could provide a good trade-off between the effects of improved resolution and improved contrast while keeping the dynamic range linearity unaltered.

Resolution and contrast improved ultrafast power Doppler microvessel imaging with null subtraction imaging

In this work, we demonstrate a novel non-linear beamforming technique, called null-subtraction imaging (NSI), to improve spatial resolution and image contrast of ultrafast, power Doppler microvessel imaging without significantly increasing computational cost compared to traditional delay and sum (DAS). NSI is a non-linear beamforming technique that operates on receive data by subtracting envelopes of beamforming results from three apodization windows. An array transducer and Verasonics Vantage 256 system were used to capture 1600 frames of raw ultrasonic radio frequency (RF) channel data by scanning a rat brain using nine plane waves spanning angles between -4° and 4° at a pulse repetition frequency of 1000 Hz. A singular value decomposition filter was applied on the raw RF channel data to filter out the tissue signal. Coherent compounding was performed individually on the beamformed result for each apodization window. Next, the subtraction of the envelopes for each apodization was conducted to form the NSI image. A total of 1,600 frames of NSI images were accumulated to form the final image. The NSI based ultrafast power Doppler microvessel imaging provided a ten-fold improvement in spatial resolution and a three-fold improvement in image contrast compared with the traditional DAS-based ultrafast power Doppler microvessel imaging.

Nonlinear Beamforming Based on Amplitude Coherence Applied to Ultrasonic Imaging of Coarse-Grained Steels

Abstract This paper deals with ultrasonic imaging in a nondestructive evaluation (NDE) context. In particular, we are focused on the inspection of coarse-grained steels having a heterogeneous composition that creates structural noise in the ultrasonic signals and images. The standard way to beamform the acquired ultrasonic data is by delay-and-sum (DAS). This method is fast but suffers from low signal-to-noise ratio (SNR) for coarse-grained steel inspection. In this paper, we propose to adapt a coherence-based beamformer called pDAS from the medical imaging community. pDAS beamforming is based on DAS structure but includes p-root and p-power before and after summations, respectively. It results in an enhancement of the coherent summation of signals that improves both resolution and contrast. Coherence-based beamformers are known to enhance information whose acoustic response correlates with geometrical information, that is why they decrease grating lobes and side lobes, specular echoes, reconstruction artifacts, and noise due to multiple scattering. In this paper, the pDAS beamformer is proposed for two common acquisition schemes employed in NDE that are plane wave imaging (PWI) and full matrix capture (FMC). The beamformers have been efficiently implemented for parallel computing on graphics processing unit (GPU) in a context of real-time imaging and fast part scanning in NDE. First, experimental results are presented from an austenitic-ferritic sample from the power generation industry that contains side drilled holes (SDH) with diameter 0.4 mm at several depths. pDAS (for p from two to three) shows improvements in terms of SNR and resolution compared to standard DAS, both in PWI and FMC modalities. We also show that the computation cost of pDAS is equivalent to DAS. A real application on a sample containing a fatigue crack connected to the backwall is exposed. We show that pDAS beamformer can enhance crack response compared to grains, but it also decreases unwanted information such as backwall specular echoes and reconstruction artifacts.

Grating Lobe Reduction in Plane-Wave Imaging With Angular Compounding Using Subtraction of Coherent Signals.

Plane-wave imaging (PWI) with angular compounding has gained in popularity over recent years, because it provides high frame rates and good image properties. However, most linear arrays used in clinical practice have a pitch that is equal to than the wavelength of ultrasound. Hence, the presence of grating lobes is a concern for PWI using multiple transmit angles. The presence of grating lobes produces clutter in images and reduces the ability to observe tissue contrast. Techniques to reduce or eliminate the presence of grating lobes for PWI using multiple angles will result in improved image quality. Null subtraction imaging (NSI) is a nonlinear beamforming technique that has been explored for improving the lateral resolution of ultrasonic imaging. However, the apodization scheme used in NSI also eliminates or greatly reduces the presence of grating lobes. Imaging tasks using NSI were evaluated in simulations and physical experiments involving tissue-mimicking phantoms and rat tumors in vivo. Images created with NSI were compared with images created using traditional delay and sum (DAS) with Hann apodization and images created using a generalized coherence factor (GCF). NSI was observed to greatly reduce the presence of grating lobes in ultrasonic images, compared to DAS with Hann and GCF, while maintaining spatial resolution and contrast in the images. Therefore, NSI can provide a novel means of creating images using PWI with multiple steering angles on clinically available linear arrays while reducing the adverse effects associated with grating lobes.

Enhancing 3-D Land Seismic Data Using Nonlinear Beamforming Based on the Efficiency-Improved Genetic Algorithm

Seismic data acquired in a desert environment often have a low signal-to-noise ratio, posing a significant challenge to seismic processing, imaging, and inversion. Nonlinear beamforming is one effective method that uses local second-order mathematical operators to describe seismic events and then enhance them. However, estimating the operator coefficients from input data is a nonlinear and compute-intensive optimization problem. We propose a new method for this estimation based on a recently developed efficiency-improved genetic algorithm. We demonstrate that it delivers an excellent balance between improved data quality and computational efficiency. We also introduce a “spatial consistency” feature to further speed up the algorithm by using available nonlinear-beamforming operators as initial trial solutions for the neighboring data ensembles. These findings are supported by applying the new approach to land seismic datasets from the desert environment.

A mathematical perspective of ultrasound image representations and image quality criteria

What is an ultrasound “image”? Where an engineer or physicist may see a quantitative map of physical properties, a physician may see qualitative anatomical features and pathologies. In the past, each image type was evaluated appropriately within its respective context: quantitative image quality was measured with criteria like the contrast-to-noise ratio (CNR), and qualitative images underwent dynamic range transformations to optimize human perception of contrast. Recent non-linear beamforming methods have blurred this line: the produced images are transformed like qualitative images but evaluated with quantitative criteria like CNR. Here, we identify the mathematical flaws in reasoning and suggest rigorous alternatives.An image assigns values to spatial coordinates. Let X denote the set of all possible image values. The mathematical structure endowed on X determines the set of equivalence-preserving transformations. For instance, qualitative images treat X as a general topological space, where images are equivalent under homeomorphisms of X (dynamic range transformations). Quantitative images treat X as a metric space and have fewer equivalence-preserving transformations. These structures determine when criteria like contrast, CNR, generalized CNR, and spatial resolution can be used. To extrapolate these criteria to other contexts, one must use relevant structure-preserving isomorphisms (e.g., histogram matching to preserve information content).

A nonlinear beamforming for enhanced spatiotemporal sensitivity in high frame rate ultrasound flow imaging

Typically, an ultrasound flow imaging system employs the conventional delay and sum (DAS) beamformer due to its inherent low complexity. But the conventional DAS technique offers poor contrast, low imaging resolution, and limited spatiotemporal sensitivity. This article attempts to improve the spatiotemporal sensitivity of the conventional flow imaging with a novel multiply and sum based nonlinear high-resolution (NLHR) beamforming approach. The major advantages of the proposed beamformer are the harmonic generation and the enhanced coherence in beamformed signals that improve the spatiotemporal sensitivity towards flow transients. We demonstrate the proposed beamformer for a directional cross-correlation as well as an autocorrelation based velocity estimator with simulated parabolic flow profiles of different velocities and flow directions, an in-vitro rotating disk dataset, and pulsatile flow experiments. The sensitivity of NLHR beamforming towards the flow transients is validated in-vitro with a sudden reversal of flow direction and air bubble tracking experiments. The comparison between the time–frequency plots of DAS and NLHR beamforming indicates that the impulsive spatiotemporal changes induced by the flow of air bubbles are clearly characterized by nonlinear beamforming than that of DAS beamforming. Furthermore, better spatiotemporal velocity tracking of a single air bubble and a clear distinguishability between the tracking of two proximal air bubbles are observed in-vitro. Preliminary studies on the in-vivo carotid data also show comparable, if not better, results than that of the DAS algorithm. Detailed results for each test case in simulation, phantom, and in-vivo studies are available as movies with the supplementary material and online [Online Link].

Accelerating the 2+2+1 method for estimating local traveltime operators in nonlinear beamforming using GPU graphics cards

Abstract Local traveltime operators are an effective way to describe local kinematic wavefronts. They are useful for many applications. One of them is nonlinear beamforming for enhancing the signal-to-noise ratio of challenging seismic data. The so-called 2+2+1 method is a pragmatic approach to estimate unknown local traveltime operators from input data. However, its efficiency still has much room for improvement when the solution space is big. We accelerate the 2+2+1 method using graphics processing unit (GPU) computing with the Compute Unified Device Architecture (CUDA) programming language. We detail the CPU- and GPU-based 2+2+1 search algorithms and demonstrate the efficiency improvement using synthetic and field data examples. Compared to a standard multi-core CPU implementation, our new GPU implementation achieves almost the same quality results at only ∼10% run-time cost.

Ultrasonic pseudo-color imaging in strongly attenuating materials with Filtered-Delay Multiply And Sum nonlinear beamforming

To detect flaws in strongly attenuating materials, we propose an ultrasonic phased array imaging method that combines Filtered-Delay Multiply And Sum (F-DMAS) nonlinear beamforming algorithm with pseudo-color technique. Based on the spatial coherence of signals, three filters with different frequency ranges are selected to reconstruct F-DMAS images from the full matrix capture (FMC) data. Then, three channels of F-DMAS images are combined with the RGB color model to obtain the pseudo-color image. Finally, an automatic flaw extraction algorithm is developed using the techniques of color image segmentation, data fusion, and edge detection. Experiments are performed on samples of polymer bonded explosives with side drilled holes. The results show that the proposed method has significant advantages over the linear beamformed Total Focusing Method (TFM) in terms of signal-to-noise ratio, detection ability, and visual presentation of flaws.

Characterizing shallow subsurface using 3D seismic while drilling with a downhole pilot

Seismic while drilling (SWD) can provide high-resolution subsurface information and characterize near-surface geology. We present a case study of SWD analysis using a data set from a desert environment acquired over a complex overburden. The data were acquired with a system composed of wireless surface geophones as well as top-drive and downhole sensors. The drill-bit noise data were reprocessed using a specialized workflow with two essential elements. First, a downhole pilot from a near-bit sensor was used for deconvolution, which led to improved data quality, particularly in the shallow subsurface. Second, nonlinear beamforming leveraged the 3D carpet of geophones to enhance signal quality and enable picking 3D traveltimes. A simple workflow for building a 1D velocity model used 3D traveltimes from an offset of 180 to 500 m. We vertically projected and averaged all 3D traveltimes to obtain a robust checkshot profile for the section from 190 to 1855 m. For the shallow subsurface (0–800 m), we further applied an advanced workflow with 3D traveltime inversion that more accurately handled mid- and far-offset data using a ray-tracing engine. More than 100,000 offset traveltime picks were inverted for a 1D velocity model. The model closely ties with the geology of the near surface, namely the formation tops associated with major impedance and lithologic contrasts. Amplitude signatures of 3D SWD gathers also correlate with the velocity model and lithologic changes, showing weak energy associated with soft formations and higher-energy first-arrival waveforms associated with compacted formations. Finally, we used the data extracted from a 2D line to reconstruct a migrated image of the back-propagated drill-bit sources. Joint use of kinematic and dynamic signatures helps characterize markers associated with loss circulation zones and target layers.

Ultrasound Localization Microscopy in Liquid Metal Flows

Liquid metal convection plays an important role in natural and technical processes. In experimental studies, an instrumentation with a sub-millimeter spatial resolution is required in an opaque fluid to resolve the flow field near the boundary layer. Using ultrasound methods, the trade-off between the frequency and imaging depth of typical laboratory experiments limits the spatial resolution. Therefore, the method of ultrasound localization microscopy (ULM) was introduced in liquid metal experiments for the first time in this study. To isolate the intrinsic scattering particles, an adaptive nonlinear beamformer was applied. As a result, an average spatial resolution of 188 μm could be achieved, which corresponded to a fraction of the ultrasound wavelength of 0.28. A convection experiment was measured using ULM. Due to the increased spatial resolution, the high-velocity gradients and the recirculation areas of a liquid metal convection experiment could be observed for the first time. The presented technique paves the way for in-depth flow studies of convective turbulent liquid metal flows that are close to the boundary layer.

Evaluating strategies for estimation of local kinematic parameters in noisy land data: quality versus performance trade-offs

Abstract Modern land seismic data are typically acquired using high spatial trace density with small source and receiver arrays or point sources and sensors. These datasets are challenging to process due to their massive size and relatively low signal-to-noise ratio caused by scattered near-surface noise. Therefore, prestack data enhancement becomes a critical step in the processing flow. Nonlinear beamforming had proved very powerful for 3D land data. However, it requires computationally intensive estimations of local coherency on dense spatial/temporal grids in 3D prestack data cubes. We present an analysis of various estimation methods focusing on a trade-off between computational efficiency and enhanced data quality. We demonstrate that the popular sequential «2 + 2 + 1» scheme is highly efficient but may lead to unreliable estimation and poor enhancement for data with a low signal-to-noise ratio. We propose an alternative algorithm called «dip + curvatures» that remains stable for such challenging data. We supplement the new strategy with an additional interpolation procedure in spatial and time dimensions to reduce the computational cost. We demonstrate that the «dip + curvatures» strategy coupled with an interpolation scheme approaches the «2 + 2 + 1» method's efficiency while it significantly outperforms it in enhanced data quality. We conclude that the new algorithm strikes a practical trade-off between the performance of the algorithm and the quality of the enhanced data. These conclusions are supported by synthetic and real 3D land seismic data from challenging desert environments with complex near surface.