Spatial and temporal aberrator stability for real-time adaptive imaging

Spatial Ambiguity Correction in Coherence-Based Average Sound Speed Estimation

Sound speed estimation can potentially correct the focusing errors in medical ultrasound. Maximizing the echo spatial coherence as a function of beamforming sound speed is a known technique to estimate the average sound speed. However, beamformation with changing sound speed causes a spatial shift of the echo signals resulting in noise and registration errors in the average sound speed estimates. We show that the spatial shift can be predicted and corrected, leading to superior sound speed estimates. Methods are presented for axial and 2-D location correction. Methods were evaluated using simulations and experimental phantom data. The location correction strategies improved the variance of sound speed estimates and reduced artifacts in the presence of strong backscatter variations. Limitations of the proposed methods and potential improvement strategies were evaluated.

Improved Transcranial Plane-Wave Imaging With Learned Speed-of-Sound Maps

Although transcranial ultrasound plane-wave imaging (PWI) has promising clinical application prospects, studies have shown that variable speed-of-sound (SoS) would seriously damage the quality of ultrasound images. The mismatch between the conventional constant velocity assumption and the actual SoS distribution leads to the general blurring of ultrasound images. The optimization scheme for reconstructing transcranial ultrasound image is often solved using iterative methods like full-waveform inversion. These iterative methods are computationally expensive and based on prior magnetic resonance imaging (MRI) or computed tomography (CT) information. In contrast, the multi-stencils fast marching (MSFM) method can produce accurate time travel maps for the skull with heterogeneous acoustic speed. In this study, we first propose a convolutional neural network (CNN) to predict SoS maps of the skull from PWI channel data. Then, use these maps to correct the travel time to reduce transcranial aberration. To validate the performance of the proposed method, numerical, phantom and intact human skull studies were conducted using a linear array transducer (L11-5v, 128 elements, pitch = 0.3 mm). Numerical simulations demonstrate that for point targets, the lateral resolution of MSFM-restored images increased by 65%, and the center position shift decreased by 89%. For the cyst targets, the eccentricity of the fitting ellipse decreased by 75%, and the center position shift decreased by 58%. In the phantom study, the lateral resolution of MSFM-restored images was increased by 49%, and the position shift was reduced by 1.72 mm. This pipeline, termed AutoSoS, thus shows the potential to correct distortions in real-time transcranial ultrasound imaging, as demonstrated by experiments on the intact human skull.

Windowed Radon Transform and Tensor Rank-1 Decomposition for Adaptive Beamforming in Ultrafast Ultrasound

Ultrafast ultrasound has recently emerged as an alternative to traditional focused ultrasound. By virtue of the low number of insonifications it requires, ultrafast ultrasound enables the imaging of the human body at potentially very high frame rates. However, unaccounted for speed-of-sound variations in the insonified medium often result in phase aberrations in the reconstructed images. The diagnosis capability of ultrafast ultrasound is thus ultimately impeded. Therefore, there is a strong need for adaptive beamforming methods that are resilient to speed-of-sound aberrations. Several of such techniques have been proposed recently but they often lack parallelizability or the ability to directly correct both transmit and receive phase aberrations. In this article, we introduce an adaptive beamforming method designed to address these shortcomings. To do so, we compute the windowed Radon transform of several complex radio-frequency images reconstructed using delay-and-sum. Then, we apply to the obtained local sinograms weighted tensor rank-1 decompositions and their results are eventually used to reconstruct a corrected image. We demonstrate using simulated and in-vitro data that our method is able to successfully recover aberration-free images and that it outperforms both coherent compounding and the recently introduced SVD beamformer. Finally, we validate the proposed beamforming technique on in-vivo data, resulting in a significant improvement of image quality compared to the two reference methods.

Ultrasound Matrix Imaging-Part II: The Distortion Matrix for Aberration Correction Over Multiple Isoplanatic Patches

This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals to synthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.

Accelerated 2-D Real-Time Refraction-Corrected Transcranial Ultrasound Imaging

In a recent study, we proposed a technique to correct aberration caused by the skull and reconstruct a transcranial B-mode image with a refraction-corrected synthetic aperture imaging (SAI) scheme. Given a sound speed map, the arrival times were calculated using a fast marching technique (FMT), which solves the Eikonal equation and, therefore, is computationally expensive for real-time imaging. In this article, we introduce a two-point ray tracing method, based on Fermat's principle, for fast calculation of the travel times in the presence of a layered aberrator in front of the ultrasound probe. The ray tracing method along with the reconstruction technique is implemented on a graphical processing unite (GPU). The point spread function (PSF) in a wire phantom image reconstructed with the FMT and the GPU implementation was studied with numerical synthetic data and experiments with a bone-mimicking plate and a sagittally cut human skull. The numerical analysis showed that the error on travel times is less than 10% of the ultrasound temporal period at 2.5 MHz. As a result, the lateral resolution was not significantly degraded compared with images reconstructed with FMT-calculated travel times. The results using the synthetic, bone-mimicking plate, and skull dataset showed that the GPU implementation causes a lateral/axial localization error of 0.10/0.20, 0.15/0.13, and 0.26/0.32 mm compared with a reference measurement (no aberrator in front of the ultrasound probe), respectively. For an imaging depth of 70 mm, the proposed GPU implementation allows reconstructing 19 frames/s with full synthetic aperture (96 transmission events) and 32 frames/s with multiangle plane wave imaging schemes (with 11 steering angles) for a pixel size of [Formula: see text]. Finally, refraction-corrected power Doppler imaging is demonstrated with a string phantom and a bone-mimicking plate placed between the probe and the moving string. The proposed approach achieves a suitable frame rate for clinical scanning while maintaining the image quality.

Adaptive Models for Multi-Covariate Imaging of Sub-Resolution Targets (MIST)

Multi-covariate imaging of sub-resolution targets (MIST) is a statistical, model-based image formation technique that smooths speckles and reduces clutter. MIST decomposes the measured covariance of the element signals into modeled contributions from mainlobe, sidelobes, and noise. MIST covariance models are derived from the well-known autocorrelation relationship between transmit apodization and backscatter covariance. During in vivo imaging, the effective transmit aperture often deviates from the applied apodization due to nonlinear propagation and wavefront aberration. Previously, the backscatter correlation length provided a first-order measure of these patient-specific effects. In this work, we generalize and extend this approach by developing data-adaptive covariance estimation, parameterization, and model-formation techniques. We performed MIST imaging using these adaptive models and evaluated the performance gains using 152 tissue-harmonic scans of fetal targets acquired from 15 healthy pregnant subjects. Compared to standard MIST imaging, the contrast-to-noise ratio (CNR) is improved by a median of 8.3%, and the speckle signal-to-noise ratio (SNR) is improved by a median of 9.7%. The median CNR and SNR gains over B-mode are improved from 29.4% to 40.4% and 24.7% to 38.3%, respectively. We present a versatile empirical function that can parameterize an arbitrary speckle covariance and estimate the effective coherent aperture size and higher order coherence loss. We studied the performance of the proposed methods as a function of input parameters. The implications of system-independent MIST implementation are discussed.

Refraction-Corrected Transcranial Ultrasound Imaging Through the Human Temporal Window Using a Single Probe

Transcranial ultrasound imaging (TUI) is a diagnostic modality with numerous applications, but unfortunately, it is hindered by phase aberration caused by the skull. In this article, we propose to reconstruct a transcranial B-mode image with a refraction-corrected synthetic aperture imaging (SAI) scheme. First, the compressional sound velocity of the aberrator (i.e., the skull) is estimated using the bidirectional headwave technique. The medium is described with four layers (i.e., lens, water, skull, and water), and a fast marching method calculates the travel times between individual array elements and image pixels. Finally, a delay-and-sum algorithm is used for image reconstruction with coherent compounding. The point spread function (PSF) in a wire phantom image and reconstructed with the conventional technique (using a constant sound speed throughout the medium), and the proposed method was quantified with numerical synthetic data and experiments with a bone-mimicking plate and a human skull, compared with the PSF achieved in a ground truth image of the medium without the aberrator (i.e., the bone plate or skull). A phased-array transducer (P4-1, ATL/Philips, 2.5 MHz, 96 elements, pitch = 0.295 mm) was used for the experiments. The results with the synthetic signals, the bone-mimicking plate, and the skull indicated that the proposed method reconstructs the scatterers with an average lateral/axial localization error of 0.06/0.14 mm, 0.11/0.13 mm, and 1.0/0.32 mm, respectively. With the human skull, an average contrast ratio (CR) and full-width-half-maximum (FWHM) of 37.1 dB and 1.75 mm were obtained with the proposed approach, respectively. This corresponds to an improvement of CR and FWHM by 7.1 dB and 36% compared with the conventional method, respectively. These numbers were 12.7 dB and 41% with the bone-mimicking plate.

Distortion matrix approach for ultrasound imaging of random scattering media

Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wave fronts and degrade image quality. Adaptive focusing can compensate for such aberration but is only effective over a restricted field of view. Here, we introduce a full-field approach to wave imaging based on the concept of the distortion matrix. This operator essentially connects any focal point inside the medium with the distortion that a wave front, emitted from that point, experiences due to heterogeneities. A time-reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a full-field image of the medium with diffraction-limited resolution. Importantly, this process is particularly efficient in random scattering media, where traditional approaches such as adaptive focusing fail. Here, we first present an experimental proof of concept on a tissue-mimicking phantom and then, apply the method to in vivo imaging of human soft tissues. While introduced here in the context of acoustics, this approach can also be extended to optical microscopy, radar, or seismic imaging.

A Locally Adaptive Phase Aberration Correction (LAPAC) Method for Synthetic Aperture Sequences

Phase aberration is a phenomenon caused by heterogeneity of the speed of sound in tissue, in which the actual speed of sound of the tissue is different than the assumed speed of sound used for beamforming. It reduces the quality and resolution of ultrasonic images and impairs clinical diagnostic capabilities. Although phase aberration correction (PAC) methods can reduce these detrimental effects, most practical implementations of PAC methods are based on the near field phase screen model, which have limited ability to represent the true aberration induced by inhomogeneous tissue. Accordingly, we propose a locally adaptive phase aberration correction (LAPAC) method that is applied through the use of synthetic aperture. The method is tested using full-wave simulations of models of human abdominal wall, experiments with tissue aberrators, and in vivo carotid images. LAPAC is compared with conventional phase aberration correction (cPAC) where aberration profiles are computed at a preselected depth and applied to the beamformer's time delays. For all experiments, LAPAC shows an average of 1 to 2 dB higher contrast than cPAC, and enhancements of 3 to 7 dB with respect to the uncorrected cases. We conclude that LAPAC may be a viable option to enhance ultrasound image quality images even in the presence of clinically relevant aberrating conditions.

Effects of Phase Aberration and Phase Aberration Correction on the Minimum Variance Beamformer

The minimum variance (MV) beamformer has the potential to enhance the resolution and contrast of ultrasound images but is sensitive to steering vector errors. Robust MV beamformers have been proposed but mainly evaluated in the presence of gross sound speed mismatches, and the impact of phase aberration correction (PAC) methods in mitigating the effects of phase aberration in MV beamformed images has not been explored. In this study, an analysis of the effects of aberration on conventional MV and eigenspace MV (ESMV) beamformers is carried out. In addition, the impact of three PAC algorithms on the performance of MV beamforming is analyzed. The different beamformers were tested on simulated data and on experimental data corrupted with electronic and tissue-based aberration. It is shown that all gains in performance of the MV beamformer with respect to delay-and-sum (DAS) are lost at high aberration strengths. For instance, with an electronic aberration of 60 ns, the lateral resolution of DAS degrades by 17% while MV degrades by 73% with respect to the images with no aberration. Moreover, although ESMV shows robustness at low aberration levels, its degradation at higher aberrations is approximately the same as that of regular MV. It is also shown that basic PAC methods improve the aberrated MV beamformer. For example, in the case of electronic aberration, multi-lag reduces degradation in lateral resolution from 73% to 28% and contrast loss from 85% to 25%. These enhancements allow the combination of MV and PAC to outperform DAS and PAC and ESMV in moderate and strong aberrations. We conclude that the effect of aberration on the MV beamformer is stronger than previously reported in the literature and that PAC is needed to improve its clinical potential.

Resolution and brightness characteristics of short-lag spatial coherence (SLSC) images

We previously described a novel beamforming method that images the spatial correlation of an echo wave field with demonstrated applications to clutter reduction in high-noise environments. In this paper, several characteristics of the resolution and brightness of short-lag spatial coherence (SLSC) images formed by this method are compared with B-mode images formed by conventional delay-and-sum beamforming methods. Point target widths were measured to estimate resolution, the autocorrelation of image texture was measured to estimate texture size, and the contrast (i.e., brightness ratio) of clinically relevant targets was assessed. SLSC images demonstrate improved resolution and contrast with increasing values of channel noise and clutter, whereas B-mode resolution was degraded in the presence of high noise (i.e., > -12 dB channel noise-to-signal ratios) and high clutter magnitudes (i.e., > -21 dB relative to point target magnitude). Lateral resolution in SLSC images was improved with increasing lag value, whereas axial resolution was degraded with increasing correlation kernel length. The texture size of SLSC images was smaller than that of matched B-mode images. Results demonstrate that the resolution and contrast of coherence-based images depend on a range of parameters, but are generally superior to those of matched B-mode images under challenging imaging conditions.

Short-lag spatial coherence imaging on matrix arrays, part II: Phantom and in vivo experiments

In Part I of the paper, we demonstrated through simulation the potential of volumetric short-lag spatial coherence (SLSC) imaging to improve visualization of hypoechoic targets in three dimensions. Here, we demonstrate the application of volumetric SLSC imaging in phantom and in vivo experiments using a clinical 3-D ultrasound scanner and matrix array. Using a custom single-channel acquisition tool, we collected partially beamformed channel data from the fully sampled matrix array at high speeds and created matched Bmode and SLSC volumes of a vessel phantom and in vivo liver vasculature. 2-D and 3-D images rendered from the SLSC volumes display reduced clutter and improved visibility of the vessels when compared with their B-mode counterparts. We use concurrently acquired color Doppler volumes to confirm the presence of the vessels of interest and to define the regions inside the vessels used in contrast and contrast-to-noise ratio (CNR) calculations. SLSC volumes show higher CNR values than their matched B-mode volumes, while the contrast values appear to be similar between the two imaging methods.

Ultrasonic multipath and beamforming clutter reduction: a chirp model approach

In vivo ultrasonic imaging with transducer arrays suffers from image degradation resulting from beamforming limitations, including diffraction-limited beamforming and beamforming degradation caused by tissue inhomogeneity. Additionally, based on recent studies, multipath scattering also causes significant image degradation. To reduce degradation from both sources, we propose a model-based signal decomposition scheme. The proposed algorithm identifies spatial frequency signatures to decompose received wavefronts into their most significant scattering sources. Scattering sources originating from a region of interest are used to reconstruct decluttered wavefronts, which are beamformed into decluttered RF scan lines or A-lines. To test the algorithm, ultrasound system channel data were acquired during liver scans from 8 patients. Multiple data sets were acquired from each patient, with 55 total data sets, 43 of which had identifiable hypoechoic regions on normal B-mode images. The data sets with identifiable hypoechoic regions were analyzed. The results show the decluttered B-mode images have an average improvement in contrast over normal images of 7.3 ± 4.6 dB. The contrast-to-noise ratio (CNR) changed little on average between normal and decluttered Bmode, -0.4 ± 5.9 dB. The in vivo speckle SNR decreased; the change was -0.65 ± 0.28. Phantom speckle SNR also decreased, but only by -0.40 ± 0.03.

3-D transcranial ultrasound imaging with bilateral phase aberration correction of multiple isoplanatic patches: a pilot human study with microbubble contrast enhancement

With stroke currently the second-leading cause of death globally, and 87% of all strokes classified as ischemic, the development of a fast, accessible, cost-effective approach for imaging occlusive stroke could have a significant impact on health care outcomes and costs. Although clinical examination and standard computed tomography alone do not provide adequate information for understanding the complex temporal events that occur during an ischemic stroke, ultrasound imaging is well suited to the task of examining blood flow dynamics in real time and may allow for localization of a clot. A prototype bilateral 3-D ultrasound imaging system using two matrix array probes on either side of the head allows for correction of skull-induced aberration throughout two entire phased array imaging volumes. We investigated the feasibility of applying this custom correction technique in five healthy volunteers with Definity microbubble contrast enhancement. Subjects were scanned simultaneously via both temporal acoustic windows in 3-D color flow mode. The number of color flow voxels above a common threshold increased as a result of aberration correction in five of five subjects, with a mean increase of 33.9%. The percentage of large arteries visualized by 3-D color Doppler imaging increased from 46% without aberration correction to 60% with aberration correction.

Pitch-catch phase aberration correction of multiple isoplanatic patches for 3-D transcranial ultrasound imaging

Having previously presented the ultrasound brain helmet, a system for simultaneous 3-D ultrasound imaging via both temporal bone acoustic windows, the scanning geometry of this system is utilized to allow each matrix array to serve as a correction source for the opposing array. Aberration is estimated using cross-correlation of RF channel signals, followed by least mean squares solution of the resulting overdetermined system. Delay maps are updated and real-time 3-D scanning resumes. A first attempt is made at using multiple arrival time maps to correct multiple unique aberrators within a single transcranial imaging volume, i.e., several isoplanatic patches. This adaptive imaging technique, which uses steered unfocused waves transmitted by the opposing, or beacon, array, updates the transmit and receive delays of 5 isoplanatic patches within a 64° x 64° volume. In phantom experiments, color flow voxels above a common threshold have also increased by an average of 92%, whereas color flow variance decreased by an average of 10%. This approach has been applied to both temporal acoustic windows of two human subjects, yielding increases in echo brightness in 5 isoplanatic patches with a mean value of 24.3 ± 9.1%, suggesting that such a technique may be beneficial in the future for performing noninvasive 3-D color flow imaging of cerebrovascular disease, including stroke.

Harmonic spatial coherence imaging: an ultrasonic imaging method based on backscatter coherence

We introduce a harmonic version of the short-lag spatial coherence (SLSC) imaging technique, called harmonic spatial coherence imaging (HSCI). The method is based on the coherence of the second-harmonic backscatter. Because the same signals that are used to construct harmonic B-mode images are also used to construct HSCI images, the benefits obtained with harmonic imaging are also obtained with HSCI. Harmonic imaging has been the primary tool for suppressing clutter in diagnostic ultrasound imaging, however secondharmonic echoes are not necessarily immune to the effects of clutter. HSCI and SLSC imaging are less sensitive to clutter because clutter has low spatial coherence. HSCI shows favorable imaging characteristics such as improved contrast-to-noise ratio (CNR), improved speckle SNR, and better delineation of borders and other structures compared with fundamental and harmonic B-mode imaging. CNRs of up to 1.9 were obtained from in vivo imaging of human cardiac tissue with HSCI, compared with 0.6, 0.9, and 1.5 in fundamental B-mode, harmonic B-mode, and SLSC imaging, respectively. In vivo experiments in human liver tissue demonstrated SNRs of up to 3.4 for HSCI compared with 1.9 for harmonic B-mode. Nonlinear simulations of a heart chamber model were consistent with the in vivo experiments.

Short-lag spatial coherence of backscattered echoes: imaging characteristics

Conventional ultrasound images are formed by delay-and-sum beamforming of the backscattered echoes received by individual elements of the transducer aperture. Although the delay-and-sum beamformer is well suited for ultrasound image formation, it is corrupted by speckle noise and challenged by acoustic clutter and phase aberration. We propose an alternative method of imaging utilizing the short-lag spatial coherence (SLSC) of the backscattered echoes. Compared with matched B-mode images, SLSC images demonstrate superior SNR and contrast-to-noise ratio in simulated and experimental speckle-generating phantom targets, but are shown to be challenged by limited point target conspicuity. Matched B-mode and SLSC images of a human thyroid are presented. The challenges and opportunities of real-time implementation of SLSC imaging are discussed.

Lesion detectability in diagnostic ultrasound with short-lag spatial coherence imaging

We demonstrate a novel imaging technique, named short-lag spatial coherence (SLSC) imaging, which uses short distance (or lag) values of the coherence function of backscattered ultrasound to create images. Simulations using Field II are used to demonstrate the detection of lesions of varying sizes and contrasts with and without acoustical clutter in the backscattered data. B-mode and SLSC imaging are shown to be nearly equivalent in lesion detection, based on the contrast-to-noise ratio (CNR) of the lesion, in noise-free conditions. The CNR of the SLSC image, however, can be adjusted to achieve an optimal value at the expense of image smoothness and resolution. In the presence of acoustic clutter, SLSC imaging yields significantly higher CNR than B-mode imaging and maintains higher image quality than B-mode with increasing noise. Compression of SLSC images is shown to be required under high-noise conditions but is unnecessary under no- and low-noise conditions. SLSC imaging is applied to in vivo imaging of the carotid sheath and demonstrates significant gains in CNR as well as visualization of arterioles in the carotid sheath. SLSC imaging has a potential application to clutter rejection in ultrasonic imaging.

Comparison of 3-D multi-lag cross- correlation and speckle brightness aberration correction algorithms on static and moving targets

Phase correction has the potential to increase the image quality of 3-D ultrasound, especially transcranial ultrasound. We implemented and compared 2 algorithms for aberration correction, multi-lag cross-correlation and speckle brightness, using static and moving targets. We corrected three 75-ns rms electronic aberrators with full-width at half-maximum (FWHM) auto-correlation lengths of 1.35, 2.7, and 5.4 mm. Cross-correlation proved the better algorithm at 2.7 and 5.4 mm correlation lengths (P < 0.05). Static cross-correlation performed better than moving-target cross-correlation at the 2.7 mm correlation length (P < 0.05). Finally, we compared the static and moving-target cross-correlation on a flow phantom with a skull casting aberrator. Using signal from static targets, the correction resulted in an average contrast increase of 22.2%, compared with 13.2% using signal from moving targets. The contrast-to-noise ratio (CNR) increased by 20.5% and 12.8% using static and moving targets, respectively. Doppler signal strength increased by 5.6% and 4.9% for the static and moving-targets methods, respectively.

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

The decomposition of the time reversal operator, known by the French acronym DORT, is widely used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. In the case of point-scatterers, the theory is well understood: The number of nonzero eigenvalues is equal to the number of scatterers, and the eigenvectors correspond to the scatterers Green's function. In the case of extended objects, however, the formalism is not as simple. It is shown here that, in the Fraunhofer approximation, analytical solutions can be found and that the solutions are functions called prolate spheroidal wave-functions. These functions have been studied in information theory as a basis of band-limited and time-limited signals. They also arise in optics. The theoretical solutions are compared to simulation results. Most importantly, the intuition that for an extended objects, the number of nonzero eigenvalues is proportional to the number of resolution cell in the object is justified. The case of three-dimensional objects imaged by a two-dimensional array is also dealt with. Comparison with previous solutions is made, and an application to super-resolution of scatterers is presented.

The time-reversal operator with virtual transducers: application to far-field aberration correction

The decomposition of the time-reversal operator (DORT) is a detection and focusing technique using an array of transmit receive transducers. It can extract Green's functions of scatterers in a medium. A variant consists in transmitting focused beams (FDORT). It is shown here that the FDORT method can be interpreted as the decomposition of a time-reversal operator between an array of virtual transducers located at the transmit beams' foci and the physical array. The receive singular vectors correspond to scatterers' Green's functions expressed in the physical array while the transmit singular vectors correspond to Green's functions expressed in the virtual array. The position of the virtual array can be changed by varying the position of the foci, thus offering different points of view. Parameters and performance of some transmit schemes are discussed. Appropriately positioning the virtual transducers can simplify some problems. One application is measuring and correcting aberration in the case of a far-field phase screen model. Placing the virtual transducers near the phase screen transforms the problem in a simpler near-field phase screen problem.

The cross algorithm for phase-aberration correction in medical ultrasound images formed with two-dimensional arrays

Common-midpoint signals in the near-field signal-redundancy (NFSR) algorithm for one-dimensional arrays are acquired using three consecutive transducer elements. An all-row-plus-two-column algorithm has been proposed to implement the one-dimensional NFSR algorithm on two dimensional arrays. The disadvantage of this method is that its ambiguity profile is not linear and a timeconsuming iterative method has to be used to linearize the ambiguity profile. An all-row-plus-two-column-and-a-diagonal algorithm has also been proposed. Its ambiguity profile is linear, but it is very sensitive to noise and cannot be used. In this paper, a novel cross algorithm is proposed to implement the NFSR algorithm on two-dimensional arrays. In this algorithm, common-midpoint signals are acquired using four adjacent transducer elements, which is not available in one-dimensional arrays. Its advantage includes a linear ambiguity profile and a higher measurement signal-to-noise ratio. The performance of the cross algorithm is evaluated theoretically. The region of redundancy is analyzed. The procedure for deriving the phaseaberration profile from peak positions of cross-correlation functions between common-midpoint signals is discussed. This algorithm is tested with a simulated data set acquired with a two-dimensional array, and the result shows that the cross algorithm performs better than the all-row plus-twocolumn NFSR algorithm.

Green's function estimation in speckle using the decomposition of the time reversal operator: application to aberration correction in medical imaging

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Green's function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Green's functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Green's function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.

Direction of arrival filters for improved aberration estimation

Successful adaptive imaging requires accurate measurements of the aberration profile across the array surface. Two-dimensional spatial filters are used to obtain more accurate estimates of aberrating layers by suppressing wavefronts emanating from off-axis scatterers. Application of these filters to the rf signals of the individual elements rejects wavefronts arriving from angles other than the look direction of the array and results in an increase in element-to-element correlation. Spatial filtering reduced the amount of error in the measured aberration profiles and adaptive spatial filtering further improved the estimates. The improvements in aberration estimation obtained with these methods are verified using simulations and experiments in tissue-mimicking phantoms. The technique is applied to signals obtained from in vivo human thyroid.

Phase aberration correction using ultrasound radiation force and vibrometry optimization

We describe a phase aberration correction method that uses dynamic ultrasound radiation force to harmonically vibrate an object using amplitude modulated continuous wave ultrasound. The phase of each element of an annular array transducer is adjusted to maximize the radiation force and obtain optimal focus of the ultrasound beam. The maximization of the radiation force is performed by monitoring the velocity of scatterers in the focus region. We present theory that shows focal optimization with radiation force has a well-behaved cost function. Experimental validation is shown by correction of manual defocusing of an annular array as well as correcting for a lens-shaped aberrator placed near the transducer. A Doppler laser vibrometer and a pulse-echo Doppler ultrasound method were used to monitor the velocity of a sphere used as a target for the transducer. By maximizing the radiation force-induced vibration of scatterers in the focal region, the resolution of the ultrasound beam can be recovered after aberration defocusing.

Adaptive imaging on a diagnostic ultrasound scanner at quasi real-time rates

Constructing an ultrasonic imaging system capable of compensating for phase errors in real-time is a significant challenge in adaptive imaging. We present a versatile adaptive imaging system capable of updating arrival time profiles at frame rates of approximately 2 frames per second (fps) with 1-D arrays and up to 0.81 fps for 1.75-D arrays, depending on the desired near-field phase correction algorithm. A novel feature included in this system is the ability to update the aberration profile at multiple beam locations for 1-D arrays. The features of this real-time adaptive imaging system are illustrated in tissue-mimicking phantoms with physical near-field phase screens and evaluated in clinical breast tissue with a 1.75-D array. The contrast-to-noise ratio (CNR) of anechoic cysts was shown to improve dramatically in the tissue-mimicking phantoms. In breast tissue, the width of point-like targets showed significant improvement: a reduction of 26.2% on average. Brightness of these targets, however, marginally decreased by 3.9%. For larger structures such as cysts, little improvement in features and CNR were observed, which is likely a result of the system assuming an infinite isoplanatic patch size for the 1.75-D arrays. The necessary requirements for constructing a real-time adaptive imaging system are also discussed.

Phase-aberration correction with a 3-D ultrasound scanner: feasibility study

We tested the feasibility of using adaptive imaging, namely phase-aberration correction, with two-dimensional (2-D) arrays and real-time, 3-D ultrasound. Because of the high spatial frequency content of aberrators, 2-D arrays, which generally have smaller pitch and thus higher spatial sampling frequency, and 3-D imaging show potential to improve the performance of adaptive imaging. Phase-correction algorithms improve image quality by compensating for tissue-induced errors in beamforming. Using the illustrative example of transcranial ultrasound, we have evaluated our ability to perform adaptive imaging with a real-time, 3-D scanner. We have used a polymer casting of a human temporal bone, root-mean-square (RMS) phase variation of 45.0 ns, full-width-half-maximum (FWHM) correlation length of 3.35 mm, and an electronic aberrator, 100 ns RMS, 3.76 mm correlation, with tissue phantoms as illustrative examples of near-field, phase-screen aberrators. Using the multilag, least-squares, cross-correlation method, we have shown the ability of 3-D adaptive imaging to increase anechoic cyst identification, image brightness, contrast-to-speckle ratio (CSR), and, in 3-D color Doppler experiments, the ability to visualize flow. For a physical aberrator skull casting we saw CSR increase by 13% from 1.01 to 1.14, while the number of detectable cysts increased from 4.3 to 7.7.