System and method for power-efficient retrospective transmit beamformer in range-doppler frequency domain

Abstract

Methods and systems are described for a power-efficient, retrospective transmit beamformer (RTB) that operates in the range-Doppler (RD) frequency domain and is capable of producing high-resolution, clinically relevant ultrasound images. This method, named the Range Doppler Algorithm Retrospective Transmit Beamformer (RDA RTB) can process receive channel signals from diverging waves and focused transmit sequences typically used in full-size clinical ultrasound scanners. RDA RTB achieves clinical image quality comparable to that of DAS RTB, as implemented and optimized by scanner manufacturers, while reducing CPU power consumption.

Description

SYSTEM AND METHOD FOR POWER-EFFICIENT RETROSPECTIVE TRANSMIT BEAMFORMER IN RANGE-DOPPLER FREQUENCY DOMAINCross Reference to Related Applications

[0001] The present application is based on, claims priority to, and incorporates herein by reference in its entirety for all purposes, US Provisional Application Serial No. 63 / 697,561, filed September 22, 2024.Statement of Government Support

[0002] Not applicable.Background

[0003] Recent developments in point-of-care ultrasound (POCUS) systems, including handheld ultrasound devices have led to increased demand for more power-efficient ultrasound beamformers. In particular, high portability and low cost of POCUS devices put constraints on their size, weight, and power supply, which in turn can limit the processing resources available, causing a loss in image resolution and frame rate.

[0004] Ultrasound systems usually create images using the delay-and-sum (DAS) beamformer, which focuses each pixel in the image separately, making it computationally inefficient. The computing load of DAS can be especially high when used for synthetic aperture (SA) processing, such as in retrospective transmit beamformer (RTB), which is utilized on many full-size, clinical ultrasound systems to create high-resolution images from focused transmits and diverging waves.

[0005] Thus, there is a need for improved systems and methods for POCUS ultrasound systems to meet the increased demand for high-resolution ultrasound images.Summary

[0006] The present disclosure provides systems and methods that overcome the aforementioned drawbacks by providing system and methods for reducing power consumption while preserving image quality and target visualization to make RTB a practical option for a broader array of commercial and clinical ultrasound systems.

[0007] In one aspect of the present disclosure, a method of reconstructing ultrasound images is provided. The method comprises, via a processor, (a) receiving signal from a plurality of receiveelements of an ultrasound system, (b) migrating the signal to one or more virtual sources (VS), (c) performing a two-dimensional (2-D) Fast Fourier Transform (FFT) along the one or more VS (as the first dimension) and along the plurality of receive elements (as the second dimension), (d) performing range cell migration correction (RCMC) on the signals transformed in (c), (e) applying a 2-D matched filter to the signal correct in (d) along the first dimension and the second dimension, (f) performing a 2-D inverse FFT (IFFT) on the signal filtered in (e) in the first dimension and the second dimension to produce beamformed signal, and (g) reconstructing the ultrasound image from the beamformed signal in (f). The method further comprises (h) displaying the ultrasound image on a display system.

[0008] In another aspect of the present disclosure, an image processing system is provided. The system comprises a processor, a non-transitory memory storing instructions, and a display system. When executed, the instructions cause the processor to (a) receive signal from a plurality of receive elements of an ultrasound system, (b) migrate the signal to one or more virtual sources (VS), (c) perform a two-dimensional (2-D) FFT along a first dimension of the one or more VS and along a second dimension of the plurality of receive elements, (d) performing range cell migration correction (RCMC) on the signal transformed in (c), (e) apply a 2-D matched filter to the migrated signal corrected in (d) along the first dimension and the second dimension, (f) performing a 2-D inverse FFT (IFFT) on the signal filtered in (e) in the first dimension and the second dimension to produce beamformed signal, and (g) reconstruct the ultrasound image from the beamformed signal in (f). The display system is configured to (h) display the ultrasound image.

[0009] These aspects are nonlimiting. Other aspects and features of the systems and methods described herein will be provided below.Brief Description of the Drawings

[0010] Some embodiments of the disclosure are described herein with reference to the accompanying figures which make apparent to a person having ordinary skill in the art how some embodiments of the disclosure may be practiced. The figures are for the purpose of illustrative discussion and no attempt is made to show structural details of an embodiment in more detail than is necessary for a fundamental understanding of the teachings of the disclosure.Nor are they shown to scale. Where dimensions are given in the text or figures, these dimensions are merely exemplary and do not limit the scope or spirit of the disclosed invention.

[0011] FIG. 1A is a schematic showing how RTB combines data from overlapping transmit beams.

[0012] FIG. IB is a schematic of retrospective transmit beamforming (RTB) with a focused transmit acquisition. Transmit foci are modeled as virtual sources (VS), and echoes from overlapping transmit beams are aligned according to the wave travel paths. Travel times are computed from the center of the transmit aperture to the virtual source, to the scatterer / image pixel, and back to the receive element.

[0013] FIG. 1C is a schematic of RTB with diverging waves, with virtual sources placed behind the aperture. Travel times are computed from the center of the transmit aperture to the virtual source, to the scatterer / image pixel, and back to the receive element.

[0014] FIG. 2 is a block diagram of a non-limiting example ultrasound system that may implement the systems and methods of the present disclosure.

[0015] FIG. 3 is a flow chart of the Range Doppler Algorithm for retrospective transmit beamforming (RDA RTB), designed to create high resolution images from focused transmits and diverging waves. Signals are first migrated to transmit foci (i.e. virtual sources), setting a new reference time for the signals, and the multistatic version of RDA is applied. Data space at each step is labeled below the operation.

[0016] FIG. 4A is a series of ultrasound images showing range cell migration correction (RCMC). Range cell migration correction (RCMC) migrates overlapping wavefronts together, reducing the number of computations over DAS.

[0017] FIG. 4B is a series of images showing the matched filtering step, as described herein.

[0018] FIG. 5 A is a set of B-mode images of simulated point targets, starting at 10 mm depth and spaced in 10 mm axial increments. The pre-beamformed channel data was simulated for focused transmits, and the images are reconstructed using DAS and RDA implementations of retrospective transmit beamforming (RTB). A conventional B-mode image beamformed using dynamic receive DAS (i.e. without combining the data from different transmits) is also shown as reference. All images are log compressed and displayed over 50 dB dynamic range. The images from different RTB beamformers appear similar, and they display tighter point spread functions at depths past 50mm compared to the dynamic receive DAS image.

[0019] FIG. 5B is a set of B-mode images of simulated point targets, starting at 10 mm depth and spaced in 10 mm axial increments. The pre-beamformed channel data was simulated for diverging waves, and the images are reconstructed using DAS and RDA implementations of retrospective transmit beamforming (RTB). All images are log compressed and displayed over 50 dB dynamic range. The images from different RTB beamformers appear similar, and they display tighter point spread functions at depths past 50mm compared to the dynamic receive DAS image.

[0020] FIG. 6 is a set of B-mode images of a tissue-mimicking phantom beamformed with DAS and RDA implementations of RTB. The data is acquired using a linear (focused transmit) scan with a clinical ultrasound system, and the DAS images are beamformed using the optimized MATLAB code provided by the manufacturer. The images from different beamformers show similar point target size and lesion contrast. The lesions and background regions used to compute contrast are denoted in white and red lines respectively. All images are log compressed and displayed using a dynamic range of 60 dB. The scale bar in the DAS RTB images is 5 mm.

[0021] FIG. 7A is a plot of central processing unit (CPU) power consumption measured for different beamforming algorithms as functions of time. The CPU metrics are recorded during the reconstruction of the phantom images in FIG. 6. The CPU power levels are similar between different algorithms during runtime, except the runtime for frequency-domain beamformers (RDA) is shorter than for DAS, and the total energy consumed per frame by such beamformers is therefore lower.

[0022] FIG. 7B is a plot of the CPU temperature increase measured for different beamforming algorithms as functions of time. The CPU metric is recorded during the reconstruction of the phantom images of FIG. 6.

[0023] FIG. 8 is a set of B-mode images from in vivo abdominal scans on a healthy volunteer. Specifically, a longitudinal view of the gallbladder (denoted with triangle) displays anechoic gallbladder lumen and hyperechoic gallbladder wall. Hyperechoic rib cortex (denoted with arrow) and posterior acoustic shadow can be visualized in the right upper comer of the image. Portal vein branches (denoted with cross-marks) can be seen in the lower part of FOV.Detailed Description

[0024] Systems using retrospective transmit beamforming (RTB) utilize coherent summation of data from overlapping transmit beams after the data capture, so a larger effective transmit aperture can be “synthesized” and dynamically focused across the field of view (FOV). The concept of RTB is similar to synthetic aperture (SA) focusing with virtual sources (VS), which treats transmit foci as virtual point sources, allowing the receive element signals from different transmits to be coherently summed together. While RTB and VS focusing improve image resolution away from the focal zone, combining signals from different transmits requires additional delays, making these SA techniques significantly more expensive than the traditional, dynamic-receive DAS, which processes data from one transmit per image line.

[0025] Retrospective transmit beamforming (RTB) Reconstruction with delay-and-sum (DAS)

[0026] In a non-limiting example, when a transmit focus is treated as a virtual source, pulse echo travel times for scatterers located away from the focus are given by the following expressions:- total ^tx ±vs+ T-rx (2)

[0027] In (1), Ttxdenotes the wave travel time from the center of the transmit aperture to the focus (i.e. virtual source - VS), TVSis the travel time from the VS to the scatterer, and Trxand is the receive travel time from the scatterer to the receive element. The sign of TVSis positive when z0> zvsand negative when z0< zvs. The wave propagation model given by expressions (1) and (2) is illustrated in FIG. IB. Computing the travel times in (2) for focused transmit acquisition allows a coherent summation of the receive signals from the overlapping transmit beams as shown in FIG. 1 A.

[0028] In a different non-limiting example, diverging waves are created by applying the transmit delays that place virtual sources behind the aperture, as shown in FIG. 1C. In such case, the total travel time is given by - total ~ T-tx Tvs+ Trx(3)

[0029] Here, Ttxis negative because the virtual sources are located behind the aperture. Because the reconstructed pixels are below the transducer (and thus zvs> z0), the sign of TVSin (3) is positive. Plane-wave transmit, as a special case of a diverging wave with acoustic source placed far behind the aperture is not considered here and will be part of future work.

[0030] To reconstruct DAS RTB images at real-time rates, hardware acceleration is typically used in form of Field-programmable gated arrays (FPGAs), or graphics processing units (GPUs), which can increase power consumption and cause heating, requiring additional power supply and / or active cooling to maintain safe and stable operation of the device.

[0031] Thus, while RTB has been used on some commercial ultrasound scanners to generate high-resolution images, they suffer from substantial limitations. As will be described, the present disclosure provides system and methods that reduce power consumption and preserve image quality compared to existing methods. Further, the systems and methods provided herein reduce power consumption while preserving image quality and target visualization. Thus, the systems and methods provided herein make RTB substantially more practical and economical (both in terms of financial cost and computational efficiency). Furthermore, this is the first time that a frequency -domain beamforming method (e.g., RD A) can be used to reduce power consumption on ultrasound devices.

[0032] The present disclosure recognizes that beamforming ultrasound signals in the (spatial) frequency domain can reduce the number of computations compared to DAS, as it enables focusing of received signals at many pixels simultaneously (also known as block-based beamforming).

[0033] illustrates an example of an ultrasound system 100 that can implement the methods described in the present disclosure. The ultrasound system 100 includes a transducer array 102 that includes a plurality of separately driven transducer elements 104. The transducer array 102 can include any suitable ultrasound transducer array, including linear arrays, curved arrays, phased arrays, and so on. Similarly, the transducer array 102 can include a ID transducer, a 1.5D transducer, a 1.75D transducer, a 2D transducer, a 3D transducer, and so on.

[0034] When energized by a transmitter 106, a given transducer element 104 produces a burst of ultrasonic energy. The ultrasonic energy reflected back to the transducer array 102 (e.g., an echo) from the object or subject under study is converted to an electrical signal (e.g., an echo signal) by each transducer element 104 and can be applied separately to a receiver 108 through a set ofswitches 110. The transmitter 106, receiver 108, and switches 110 are operated under the control of a controller 112, which may include one or more processors. As one example, the controller 112 can include a computer system.

[0035] The transmitter 106 can be programmed to transmit unfocused or focused ultrasound waves. In some configurations, the transmitter 106 can also be programmed to transmit diverged waves, spherical waves, cylindrical waves, plane waves, or combinations thereof. Furthermore, the transmitter 106 can be programmed to transmit spatially or temporally encoded pulses.

[0036] The receiver 108 can be programmed to implement a suitable detection sequence for the imaging task at hand. In some embodiments, the detection sequence can include one or more of line-by-line scanning, compounding plane wave imaging, synthetic aperture imaging, and compounding diverging beam imaging.

[0037] In some configurations, the transmitter 106 and the receiver 108 can be programmed to implement a high frame rate. For instance, a frame rate associated with an acquisition pulse repetition frequency (“PRF”) of at least 100 Hz can be implemented. In some configurations, the ultrasound system 100 can sample and store at least one hundred ensembles of echo signals in the temporal direction.

[0038] The controller 112 can be programmed to design an imaging sequence using the techniques described in the present disclosure, or as otherwise known in the art. In some embodiments, the controller 112 receives user inputs defining various factors used in the design of the imaging sequence.

[0039] A scan can be performed by setting the switches 110 to their transmit position, thereby directing the transmitter 106 to be turned on momentarily to energize transducer elements 104 during a single transmission event according to the designed imaging sequence. The switches 110 can then be set to their receive position and the subsequent echo signals produced by the transducer elements 104 in response to one or more detected echoes are measured and applied to the receiver 108. The separate echo signals from the transducer elements 104 can be combined in the receiver 108 to produce a single echo signal.

[0040] The echo signals are communicated to a processing unit 114, which may be implemented by a hardware processor and memory, to process echo signals or images generated from echo signals. Images produced from the echo signals by the processing unit 114 can be displayed on a display system 116.

[0041] RTB Reconstruction with RDA

[0042] The RDA has been originally developed to beamform monostatic radar signals. In the present disclosure, the signal model and key processing steps of multistatic RDA to derive RDA RTB for focused transmits and diverging waves.

[0043] Specifically, pulses emanating from virtual sources and detected by receive elements can be represented as the following baseband complex signal: s = Aowr(t - rtotai) x exp[-j2nf0Ttotal] (4) here Aois the signal amplitude, wris the signal envelope in time (range) dimension, and f0is the transmit center frequency. The pulse-echo travel timestotaiare defined in (2) and (3) for the focused transmit case and diverging waves, respectively, and can be separated into two parts: the time to create a VS (rtx), and the time that accounts for the multistatic acquisition from the VS to the scatterer, and from the scatterer back to receive elements (TVS-I- Trx). The first step of RDARTB is therefore to migrate the receive signals to virtual sources (i.e. transmit foci), followed by the multi static RDA. The key steps of RD A RTB are outlined in the example workflow 300 of FIG. 3 and are explained in greater detail below.

[0044] Step 302: Migrate the receive channel signals to virtual sources (i.e. transmit foci). As used herein, VS refers to transmit focus. In a non-limiting example, the transmit focus may be placed below the transducer array as in a typical focused transmit sequence, or behind the transducer aperture as in the case of diverging waves. Receive channel signals from different transmits are delayed to account for travel times from the centers of the transmit apertures to the VS locations (Ttx). In practice, if the virtual sources are at the same depth (as is the case with transmit foci in standard linear scan), the travel times to the VS can be accounted for by shifting the time axis, instead of shifting the data via interpolation. In that case, the first step does not increase significantly the computational load of the algorithm. The signals with the new time zero (at the focal depth) can be represented using the multistatic model in time-space domainwhere xvsand xr:,:are VS and receive element positions, respectively, / is the receive-echo time, wris the signal envelope in range / time dimension, fo is the (center) transmit frequency, and c is the wavespeed in the medium.

[0045] In (5), Rvs(xvs') and Rrxxrx)arethe wave travel paths defined in (1) and illustrated in FIGS. 1A-1C.

[0046] Step 304: Perform a two-dimensional (2-D) Fast Fourier Transform (FFT) along a first dimension of the one or more VS and a second dimension of the plurality of receive elements. Taking a 2-D FFT of the signal in (5) and applying the principle of stationary phase (POSP) to find the analytic solution to the integrals results in the multistatic signal model in RD domainwhere kvsand krxare the spatial frequencies along the VS and receive element dimensions, respectively. The travel distances in RD domain are given aswhere Ro= z0— zvsis the scatterer depth measured relative to VS.

[0047] Step 306: Perform Range Cell Migration Correction (RCMC). The range cell migration correction migrates the range envelopes wracross the spatial frequencies. In the RD domain, scatterers that are located at the same depth will have overlapping wavefronts and can be migrated together, providing a speedup over time-domain beamformers (such as DAS) that have to migrate wavefronts at each pixel separately. A non-limiting advantage of performing RCMC in RD domain is illustrated in FIG. 4A. RCMC is typically implemented as a 1-D interpolation ofsignals along time / range axis, with interpolation times computed according to (7). Specifically, with DAS beamforming the channel data is processed in time-space domain, where the wavefronts originating from different pixels have to be migrated separately (FIG. 4A, top panel). In the RD domain, the wavefronts from the same depth overlap and can be migrated together (FIG. 4A, middle and bottom panels), requiring fewer computations and enabling RDA to be more efficient. The phase oscillation in RD domain is compensated for using the matched filter (FIG. 4B), which is implemented as multiplication of the signal with the azimuth impulse response (Eq. (8), below).

[0048] Step 308: Apply a 2-D matched filter along kvsand krxfrequency dimensions. Matched filtering is used to remove the azimuth phase of migrated signals. Specifically, the matched filter is computed as the complex conjugate of the phase-terms in equation (6)

[0049] The effect of matched filtering is shown on simulated monostatic data in FIG. 4B.

[0050] Step 310: Perform a 2-D inverse FFT (IFFT) along kvsand krxdimensions. An Inverse Fourier Transform converts the migrated and filtered signals from the RD domain to the (r, xvs, xrx) image space, as shown in the bottom image of FIG. 4B. To obtain a standard 2-D image, a diagonal (r, x) plane is selected along the xvsand xrxaxes.

[0051] It is noted that steps 304-310 are based on a multistatic version of RDA.

[0052] Reduced number of computations in steps 304 and 306, may lead to shorter processing times and reduced power requirements of RDA relative to DAS.

[0053] The following Example demonstrates non-limiting implementations and applications of the method and system described herein.

[0054] Example

[0055] 1. Methods

[0056] 1.1 FIELD II Simulations of Virtual Source Data

[0057] FIELD II software was used to simulate radiofrequency (RF) ultrasound signals from linear scans using focused transmits and diverging waves on a point target phantom. Focal depthof 3 cm was used when simulating the signals from focused transmits. To create diverging waves, foci were set at 2 cm behind the aperture. The phantom was designed to allow the measurement of image resolution as a function of depth for different beamforming methods. Specifically, the point targets were placed over 10 cm depth to help quantify the improvements of RTB over conventional dynamic receive focusing at large depths. The simulation parameters are listed in Table I.Table I. Parameters for the simulated linear scan.Active Aperture size 9.9mm Element Pitch 0.15mm ( {2)No. of Active Elements 64No. of Transmits 128Total Array size 29.4mmFocal (VS) depth 3, -2 cm Center Frequency 5MHzBandwidth 60%

[0058] To create high resolution B-mode images RTB was used to coherently sum the receive channel signals from different transmits. RTB was implemented using DAS and RDA migration. The images were also created using standard dynamic receive DAS as a reference. All RTB algorithms were set to beamform RF images of the same size (2857-by-192 pixels). Zeropadding was set to be half of the total array size, or 48 elements on each side of the array. All beamformers were implemented in MATLAB (MathWorks, Natick, MA) and executed on a single CPU core. Beamformed images were envelope detected, normalized by the maximum value, and displayed on a dB scale.

[0059] 1.2 Phantom Acquisitions

[0060] Individual channel signals were collected from a GE LOGIQ E10 scanner and L2-9 linear array (GE Healthcare, Waukesha, WI) while scanning a calibrated tissue-mimicking phantom (CIRS Model 040GSE, Norfolk, VA). A focused transmit sequence was used to collect the complex IQ data up to 15 cm of depth, at the transmit center frequency of 5.5 MHz. The acquisition parameters and transducer properties are summarized in Table II. The phantom was scanned in the areas containing point targets and anechoic lesions regularly spaced over a range of depths.

[0061] B-mode images were beamformed using conventional dynamic-receive DAS, RTB implemented with DAS and RDA, in a similar manner as in section 1.1 above. All IQbeamformers were implemented by the authors in MATLAB, except for the DAS RTB, which was an optimized (in MATLAB) by the scanner manufacturer. All methods were executed on a single CPU core.Table II. Acquisition parameters for the IQ data capture with the GE LOGIQ E10 and L29 linear array. _Array size 44mmElement Pitch 0.23mmNo. of Transducer Elements 192No. of Transmits 80Transmit Focal depth 10.6 cmAcquisition depth 15 cmCenter Frequency 5.5MHzSampling Frequency 8.3MHzFractional Bandwidth 60%

[0062] To optimize the RDA RTB image quality in phantoms and in vivo, RDA RTB was implemented using axial frequency binning. Specifically, the IQ pre-beamformed signals were bandpass filtered and the algorithm was executed over two frequency bins, which doubled its running time and consumed CPU energy. The beamformed RDA images from two frequency bins were summed coherently to yield the final RDA RTB image.

[0063] 1.3 In Vivo Acquisitions

[0064] Ultrasound (US) imaging was performed by an operator with 14 years of abdominal US experience and using the same FDA-cleared US system as in section 1.2 (GE LOGIQ E10 with L2-9 linear array). The operator acquired prebeamformed US data in the right upper quadrant of a 38-y ear-old healthy male volunteer, focusing mainly on the vascular and biliary structures of the liver and the right kidney.

[0065] To acquire pre-beamformed individual channel signals, the same acquisition sequences and imaging configuration were used as for the phantom experiment (section 1.2), except that for some acquisitions, harmonic data was also captured using the pulse inversion method. For harmonic acquisitions, the complex IQ channel data was collected for positive and negative transmit pulses, and the beamformed images from the two data sets were added coherently to produce a harmonic B-mode image.

[0066] 1.4 Beamformer Performance Metrics

[0067] To evaluate beamformers’ resolution and contrast, lateral profiles were taken from the simulated images at selected point target depths, allowing for direct measurements of themainlobe width and sidelobe levels. In the B-mode images of a tissue mimicking phantom, the generalized contrast- to-noise ratio (gCNR) was computed on hyperechoic and anechoic circular lesions. To compare the overall appearance of the RDA images to their DAS RTB counterparts the structural similarity index (SSIM) was computed for the phantom and in vivo acquisitions.

[0068] To assess beamformers’ speed, beamforming times were measured for the individual B- mode frames, with all beamformers implemented in MATLAB and executed on a single CPU core.

[0069] To evaluate the power efficiency of different beamforming approaches, CPU power consumption and CPU temperature increase were measured when beamforming the data from phantom and in vivo acquisitions. The CPU power consumption was recorded during runtime as output of the powerstat command in Linux terminal. The CPU temperature was reported as output of the sensor command, which is part of the publicly-available lm_sensor hardware monitoring tool on Linux. Measurements were also taken of the CPU temperature and power consumption due to background processes and they were subtracted from the values measured during runtime. The performance of RDA RTB was compared against the optimized version of DAS RTB algorithm implemented by the scanner manufacturer.

[0070] 2. Results

[0071] 2.1 Simulated Images of Point Targets

[0072] FIGS. 5A-5B show simulated point target images created from focused transmits and diverging waves. To sum the receive element signals from different transmits coherently, RTB was performed using DAS and RDA. A standard DAS image reconstructed from focused transmits using dynamic receive focusing is also shown as reference (denoted “Dynamic Rx”). All images are displayed over 50 dB of dynamic range.

[0073] At shallower depths (20 and 40 mm), the point spread functions (PSFs) are similar between different beamformers. At larger depths (beyond 50 mm), the RTB PSFs show reduced FWHM compared to the PSFs from the dynamic receive DAS (up to 2mm mainlobe reduction at 80mm depth). The RTB images created using different beamforming approaches display similar resolution at all depths, with no more than 0.1mm difference in FWHM.

[0074] The times required to beamform the images in FIG. 5A are reported in Table III. RDA RTB reduces the beamforming time approximately by a factor of three compared to DAS RTB.The reconstruction time for the dynamic receive DAS image is two orders of magnitude shorter than the reconstruction times required for the RTB images.Table III. Evaluation of the simulated images in FIG. 5A. All reconstruction methods are implemented by the authors in MATLAB and executed on a single CPU. _Evaluation Metric Dynamic Rx DAS RDAFWHM (mm)a@ 20 mm 0 / 0@ 40 mm 0.4 / 0.1@ 60 mm 1.1 / 0@ 80 mm 2.2 / 0SLLmax(dB)a@ 20 mm 0 / -4@ 40 mm 4 / -3@ 60 mm -1 / -4@ 80 mm -1 / -4 a Expressed as difference relative to DAS RTB

[0075] 2.2 Phantom Images

[0076] B-mode images from the phantom acquisitions with a clinical ultrasound system are shown in FIG. 6. The images show point targets and lesions of various sizes and intrinsic contrasts in the field of diffuse scatterers. The images are acquired using focused transmits, and beamform ed using different RTB techniques (DAS and RD A). For beamforming IQ data channel data from the clinical system, DAS RTB was implemented and optimized by the scanner manufacturer, while RDA RTB was implemented by the user. All images are displayed with 50 dB of dynamic range, and the scale bars in the DAS RTB images are 5 mm. The images from different beamformers are compared using the structural similarity index and lesion gCNR, with values listed in Table IV. Regions inside and outside the lesions used to compute gCNR are denoted with red and white dashed lines, respectively.

[0077] The three retrospective beamformers create similar speckle patterns with similar speckle sizes (FIG. 6). In FIG. 6, the width of point targets is similar between the images, except for the point targets located at larger depths (> 50mm) that appear slightly wider in the RDA RTB image than in the DAS RTB image.

[0078] Beamforming times for the images in FIG. 6 are listed in Table V. Because the RDA RTB image is reconstructed using (axial) frequency binning with two frequency bins (to reduce axial sidelobes), the algorithm is executed two times resulting in the total runtime that is 1.67 times shorter than for the industry-grade optimized DAS RTB.Table IV. Image quality metrics for DAS and RDA RTB images from the phantom acquisitions in FIG. 6.Evaluation Metric DAS RDASSIM (relative to DAS)Acq (a) - 0.90Acq (b) - 0.81 gCNRAcq (a) 0.69 0.69Acq (b) 0.88 0.80

[0079] Memory requirements for each method in FIG. 6 are also listed in Table V. Because DAS RTB code is implemented by the scanner manufacturer, the amount of memory required is measured as the size of the input data. For RDA RTB, the amount of memory required is measured as the size of the largest data variable stored during runtime. RDA requires four times and eight times more memory, respectively, than DAS RTB .Table V. Runtimes and efficiency of DAS and RDA for retrospective transmit beamforming (RTB) of the phantom images in FIG. 6. The DAS RTB code was provided by the scanner manufacturer, while the RDA RTB codes were implemented by the users. All codes were written in MATLAB and executed on a single CPU core.Evaluation Metric DAS RDABeamforming time (s) 130.1 77.8Memory required (MB) 387al,278bCPU Avg. Power (W)c13.0 ± 1.5d13.9 ± 1.7CPU Temperature (°C )c18.8 ± 2.6 18.9 ± 5.1CPU Energy spent (kJ)e1.69 1.08 a Measured as size of the input data. b Measured as size of the largest variable during runtime. c Measured as increase relative to idle CPU state. d Expressed as mean ~ standard deviation. e Energy required to reconstruct a single frame.

[0080] 2.3 Power / Temperature Measurements

[0081] FIGS. 7A-7B show the plots of CPU power consumption and CPU temperature measured during the RTB reconstructions in FIG. 6; the summary statistics is shown in Table V. The power and temperature are averaged over runtime for each algorithm, and are shown as increase relative to the idle CPU values (that are recorded before and after beamformation). During beamformation, the recorded CPU power and temperature are similar between different algorithms, but because frequency -domain beamformers (RDA) run faster, the total amount of energy they consume per frame is smaller than the energy consumed by DAS. Specifically, forthe phantom acquisition in FIG. 6, RDA RTB consumes 1 .6 times less energy than the optimized version of DAS RTB.

[0082] 2.4 In vivo Images

[0083] Annotated B-mode images from in vivo scans are shown in FIG. 8. In general, the abdominal subcutaneous layers, the structures of the liver and the right kidney are clearly visible with different reconstruction techniques (DAS RTB and RDA RTB). The longitudinal view of the gallbladder shows the anechoic lumen of the gallbladder and the hyperechoic wall of the gallbladder.

[0084] The structural similarity index measures (SSIM) of the in vivo RDA images relative to their DAS RTB counterparts are listed in Table VI, together with the beamforming times, memory, and energy consumed for each of the beam forming methods. SSIM values are relatively large (> 0.86) for all in vivo RDA RTB images, confirming their visual similarity to the matching DAS RTB images. On average, the beamforming times for the in vivo RDA RTB images are 1.65 times shorter than for the DAS RTB images. In other words, the runtime can be 40% less than reconstructing the signal running DAS RTB. Because harmonic imaging is implemented using pulse inversion and it involves beamforming separate images from positive and negative pulses, the beamforming times for the harmonic images are twice as long compared to the times for the corresponding fundamental images, while the memory requirements are the same for the fundamental and harmonic imaging modes. RDA RTB requires at least 3.5 times more memory for data storage during runtime compared to DAS RTB. For the in vivo acquisitions, RDA RTB is measured to consume 1.6 times less energy than DAS RTB on average. In other words, RDA RTB reduces the energy consumption by 38% relative to the optimized implementation of DAS RTB.Table VI. Evaluation of DAS and RDA RTB methods on in vivo images in FIG. 8. The DAS RTB code was provided by the scanner manufacturer, while the RDA RTB codes were implemented by the users. All codes were written in MATLAB and executed on a single CPU core.Evaluation Metric DAS RDASSIM (relative to DAS)Acq (a) - 0.89Acq (b) - 0.86Acq (c) - 0.89Acq (d) - 0.90Beamforming time (s)Fundamental 111.7 67.6Harmonic 222.0 152.1Memory required (MB) 356 1,263CPU Energy spent (kJ)Fundamental 1.28 0.80Harmonic 2.52 1.68

[0085] 3. Discussion

[0086] 3.1 RTB Image Quality

[0087] The above results indicate that RTB improves lateral resolution at large depths and produces a more uniform PSF across the field of view compared to conventional focused transmit beamforming. Point targets in the RTB images from simulated and phantom acquisitions (FIGS. 5A-5B and FIG. 6) appear consistent in shape over 100mm of depth. On the other hand, point targets in the simulated image reconstructed using conventional focused transmit and dynamic receive DAS (FIGS. 5A-5B) broaden progressively beyond 40mm depth (i.e. outside the transmit focal zone). Specifically, the difference in FWHM between the focused transmit image and the corresponding RTB images increases from 0.4mm to 2.2mm over the last 40mm of depth (Table III). These improvements in lateral resolution and PSF uniformity introduced by RTB are consistent with previous findings, FIGS. 6-8.

[0088] Frequency-domain implementations of RTB, including RDA RTB, achieve comparable image resolution and lesion contrast to the state-of-the-art DAS RTB approach. In the simulated acquisitions, point targets in the RDA RTB images are nearly identical to those in the corresponding DAS RTB images, with the differences in FWHM less than 0.1mm across all depths (less than A / 3 at 5 MHz; see Table III). For phantom acquisitions, DAS RTB images - beamformed using an optimized MATLAB implementation provided by the scanner manufacturer - are visually similar to their corresponding RDA RTB counterparts, with structural similarity indices (SSIM) exceeding 0.8 (Table IV). Notably, lesions in the RDA RTB images have a similar contrast as the lesions in the corresponding DAS RTB images, with the gCNR difference not exceeding 0.08 (Table IV).

[0089] It was further shown that RDA RTB is capable of producing clinically-relevant images of human tissue. Specifically, the images reconstructed from abdominal scans (FIG. 8) using RDA is visually similar to those obtained via DAS RTB, which was implemented with vendor- optimized code. The two RTB methods demonstrate comparable penetration depth and clearly delineate key abdominal structures, including the liver capsule and vasculature, and gallbladderlumen and wall. Furthermore, RD A RTB in vivo images exhibit high structural similarity to the matching DAS RTB images, with SSIM values exceeding 0.86 (Table VI).

[0090] The accuracy of frequency -domain RTB methods at large depths can be improved by taking into account frequency dependent tissue attenuation and sound-speed inhomogeneities that can change the waveform as it propagates through tissue. Current implementation of RDA RTB relies on Eq. (8) for the matched filtering step (step 308 in Fig. 3), assuming a constant center frequency and sound speed over depth. Rather than using a simple model in Eq. (8), a more accurate matched filter(s) can be implemented by simulating the aperture response (i.e. receive channel data) at different depths, while taking into account frequency-dependent attenuation and sound-speed inhomogeneities.

[0091] 3.2 Computing and Power Efficiency of RTB methods

[0092] The results demonstrate that RDA RTB reduces beamforming time and, as a result, improves power efficiency compared to DAS RTB, while preserving clinically relevant image quality and target visualization. When assuming a monochromatic signal (and using a single axial frequency bin), as in the simulated images in FIGS. 5A-5B, the beamforming times for RDA RTB are three times shorter than for DAS RTB (Table III). To reduce axial sidelobes and improve quality of phantom and in vivo scans (FIGS. 6 and 8), RDA RTB is implemented using two frequency bins, effectively doubling its runtime. As a result, for clinical scans, RDA RTB is 1.6 times faster than the optimized version of DAS RTB (Tables V and VI). Because power levels for each beamformer are relatively constant during runtime (with the standard deviation not exceeding 1.7W per Table V), power efficiency mirrors algorithm runtime, with RDA RTB able to reduce the energy consumption 1.6 times compared to DAS RTB.

[0093] Specifically, for RDA RTB, a factor of three speedup is measured on simulated data (Table V), compared to a factor of ten speedup previously reported for multistatic RDA. The differences in runtimes can be partly explained by how the RTB methods are implemented in frequency-domain. Specifically, RDA RTB processes the data from all array elements at once, even though only some elements are active during each transmission. The signals from the inactive elements are set to zero in the data matrix, which increases its size in the frequency domain. On the other hand, DAS RTB only processes the signals within the active aperture for each transmission. For example, in the simulation setup in Table I, RDA RTB uses data from all 128 receive elements, whereas DAS RTB interpolates only signals from 64 active receiveelements for each transmission. This approach is different from a multistatic beamforming setup reported previously, where signals are received on all elements for each transmit, and the number of active elements to be processed with DAS and the frequency-domain beamformers is the same, allowing frequency-domain methods to have a more significant speed advantage over DAS.

[0094] The speed advantage of RD A RTB over DAS RTB is further reduced in the phantom and in vivo acquisitions (Tables V and VI) by the fact that the DAS RTB code used to beamform data from the clinical system is highly optimized by the manufacturer. These optimizations likely include the use of precomputed interpolation coefficients, as well as aperture growth and Tx beam masking to ensure that only the necessary interpolations are performed. Moreover, to ensure a fair comparison across algorithms and minimize the influence of hardware-specific factors on beamforming time, all methods were implemented in MATLAB and executed on a single CPU core. As a result, the reported runtimes are generally much longer than those required for a real-time imaging system, and do not reflect the potential speedups if the methods were implemented in C++ or using hardware acceleration such as GPUs or FPGAs.

[0095] As used in this specification and the claims, the singular forms “a,” “an,” and “the” include plural forms unless the context clearly dictates otherwise.

[0096] As used herein, “about”, “approximately,” “substantially,” and “significantly” will be understood by persons of ordinary skill in the art and will vary to some extent on the context in which they are used. If there are uses of the term which are not clear to persons of ordinary skill in the art given the context in which it is used, “about” and “approximately” will mean up to plus or minus 10% of the particular term and “substantially” and “significantly” will mean more than plus or minus 10% of the particular term.

[0097] As used herein, the terms “include” and “including” have the same meaning as the terms “comprise” and “comprising.” The terms “comprise” and “comprising” should be interpreted as being “open” transitional terms that permit the inclusion of additional components further to those components recited in the claims. The terms “consist” and “consisting of’ should be interpreted as being “closed” transitional terms that do not permit the inclusion of additional components other than the components recited in the claims. The term “consisting essentially of’ should be interpreted to be partially closed and allowing the inclusion only of additional components that do not fundamentally alter the nature of the claimed subject matter.

[0098] The phrase “such as” should be interpreted as “for example, including.” Moreover, the use of any and all exemplary language, including but not limited to “such as”, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed.

[0099] Furthermore, in those instances where a convention analogous to “at least one of A, B and C, etc.” is used, in general such a construction is intended in the sense of one having ordinary skill in the art would understand the convention (e.g., “a system having at least one of A, B and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together.). It will be further understood by those within the art that virtually any disjunctive word and / or phrase presenting two or more alternative terms, whether in the description or figures, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”

[0100] All language such as “up to,” “at least,” “greater than,” “less than,” and the like, include the number recited and refer to ranges which can subsequently be broken down into ranges and subranges. A range includes each individual member. Thus, for example, a group having 1-3 members refers to groups having 1, 2, or 3 members. Similarly, a group having 6 members refers to groups having 1, 2, 3, 4, or 6 members, and so forth.

[0101] The modal verb “may” refers to the preferred use or selection of one or more options or choices among the several described embodiments or features contained within the same. Where no options or choices are disclosed regarding a particular embodiment or feature contained in the same, the modal verb “may” refers to an affirmative act regarding how to make or use an aspect of a described embodiment or feature contained in the same, or a definitive decision to use a specific skill regarding a described embodiment or feature contained in the same. In this latter context, the modal verb “may” has the same meaning and connotation as the auxiliary verb “can.”

Claims

Claims1. A method for reconstructing an ultrasound image, the method comprising: via a processor,(a) receiving signal from a plurality of receive elements of an ultrasound system;(b) migrating the signal to one or more virtual sources (VS);(c) performing a two-dimensional (2-D) Fast Fourier Transform (FFT) along a first dimension of the one or more VS and along a second dimension of the plurality of receive elements;(d) performing range cell migration correction (RCMC) on the signal transformed in (c);(e) applying a 2-D matched filter to the signal corrected in (d) along the first dimension and the second dimension;(f) performing a 2-D inverse FFT (IFFT) on the signal filtered in (e) in the first dimension and the second dimension to produce beamformed signal;(g) reconstructing the ultrasound image from the beamformed signal in (f); and on a display system,(h) displaying the ultrasound image.

2. The method of claim 1, wherein the signal received from the plurality of receive elements is from overlapping transmit beams of the ultrasound system.

3. The method of claim 1, wherein the signal received in (a) by each of the plurality of receive elements is delayed to account for a travel time from a plurality of transmit elements of the ultrasound system to the one or more VS.

4. The method of claim 1, wherein the signal received in (a) is ultrasound signal obtained by retrospective transmit beamforming (RTB).

5. The method of claim 4, wherein the signal is represented bywhereand kvsis the spatial frequency of a plurality of virtual sources andis the spatial frequency of the plurality of receive elements.

6. The method of claim 1, further comprising selecting a diagonal plane along a plane formed by the first dimension and second dimension to obtain the ultrasound image.

7. The method of claim 1, wherein the ultrasound image is reconstructed consuming 1.6 times or 38% less energy than reconstructing the signal using a delay and sum (DAS) approach.

8. The method of claim 1, wherein the ultrasound image is reconstructed in 40% less time than reconstructing the signal using a delay and sum (DAS) approach.

9. An image processing system, comprising: a processor; a non-transitory memory storing instructions that when executed, cause the processor to:(a) receive signal from a plurality of receive elements of an ultrasound system;(b) migrate the signal to one or more virtual sources (VS);(c) perform a two-dimensional (2-D) Fast Fourier Transform (FFT) along a first dimension of the one or more VS and along a second dimension of the plurality of receive elements;(d) perform range cell migration correction (RCMC) on the signal transformed in (c);(e) apply a 2-D matched filter to the signal corrected in (d) along the first dimension and the second dimension;(f) perform a 2-D inverse FTT (IFFT) on the signal filtered in (e) in the first dimension and the second dimension to produce beamformed signal;(g) reconstruct the ultrasound image from the beamformed signal in (f); and a display system configured to (h) display the ultrasound image.

10. The system of claim 9, wherein the signal received from the plurality of receive elements is from overlapping transmit beams of the ultrasound system.

11. The system of claim 9, wherein the signal received in (a) by each of the plurality of receive elements is delayed to account for a travel time from a plurality of transmit elements of the ultrasound system to the one or more VS.

12. The system of claim 9, wherein the signal received in (a) is ultrasound signal obtained by retrospective transmit beamforming (RTB).

13. The system of claim 12, wherein the signal is represented bywhereand kvsis the spatial frequency of a plurality of virtual sources and knis the spatial frequency of the plurality of receive elements.

14. The system of claim 9, further comprising selecting a diagonal plane along a plane formed by the first dimension and second dimension to obtain the ultrasound image15. The system of claim 9, wherein the ultrasound image is reconstructed consuming 1.6 times or 38% less energy than reconstructing the signal using a delay and sum (DAS) approach.

16. The system of claim 9, wherein the ultrasound image is reconstructed in 40% less time than reconstructing the signal using a delay and sum (DAS) approach.

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