Fast volumetric ultrasound facilitates high-resolution 3D mapping of tissue compartments.

Volumetric ultrasound imaging has the potential for operator-independent acquisition and enhanced field of view. Panoramic acquisition has many applications across ultrasound; spanning musculoskeletal, liver, breast, and pediatric imaging; and image-guided therapy. Challenges in high-resolution human imaging, such as subtle motion and the presence of bone or gas, have limited such acquisition. These issues can be addressed with a large transducer aperture and fast acquisition and processing. Programmable, ultrafast ultrasound scanners with a high channel count provide an unprecedented opportunity to optimize volumetric acquisition. In this work, we implement nonlinear processing and develop distributed beamformation to achieve fast acquisition over a 47-centimeter aperture. As a result, we achieve a 50-micrometer -6-decibel point spread function at 5 megahertz and resolve in-plane targets. A large volume scan of a human limb is completed in a few seconds, and in a 2-millimeter dorsal vein, the image intensity difference between the vessel center and surrounding tissue was ~50 decibels, facilitating three-dimensional reconstruction of the vasculature.

Adaptation of Range-Doppler Algorithm for Efficient Beamforming of Monostatic and Multistatic Ultrasound Signals.

Algorithmic changes that increase beamforming speed have become increasingly relevant to processing synthetic aperture (SA) ultrasound data. In particular, beamforming SA data in a spatio-temporal frequency domain using the F-k (Stolt) migration have been shown to reduce the beamforming time by up to two orders of magnitude compared with the conventional delay-and-sum (DAS) beamforming, and it has been used in applications where large amounts of raw data make real-time frame rates difficult to attain, such as multistatic SA imaging and plane-wave Doppler imaging with large ensemble lengths. However, beamforming signals in a spatio-temporal Fourier space can require loading large blocks of data at once, making it memory-intensive and less suited for parallel (i.e., multithreaded) processing. As an alternative, we propose beamforming in a range-Doppler (RD) frequency domain using the range-Doppler algorithm (RDA) that has originally been developed for SA radar (SAR) imaging. Through simulation and phantom experiments, we show that RDA achieves similar lateral resolution and contrast compared with DAS and F-k migration. At the same time, higher axial sidelobes in RDA images can be reduced via (temporal) frequency binning. Like the F-k migration, RDA significantly reduces the overall number of computations relative to DAS, and it achieves ten times lower processing time on a single CPU. Because RDA uses only a spatial Fourier transform (FT), it requires two times less memory than the F-k migration to process the simulated multistatic data and can be executed on as many as a thousand parallel threads (compared with eight parallel threads for the F-k migration), making it more suitable for implementation on modern graphics processing units (GPUs). While RDA is not as parallelizable as DAS, it is expected to hold a significant speed advantage on devices with moderate parallel processing capabilities (up to several thousand cores), such as point-of-care and low-cost ultrasound devices.

Distributed Aberration Correction Techniques Based on Tomographic Sound Speed Estimates.

Phase aberration is widely considered a major source of image degradation in medical pulse-echo ultrasound. Traditionally, near-field phase aberration correction techniques are unable to account for distributed aberrations due to a spatially varying speed of sound in the medium, while most distributed aberration correction techniques require the use of point-like sources and are impractical for clinical applications where diffuse scattering is dominant. Here, we present two distributed aberration correction techniques that utilize sound speed estimates from a tomographic sound speed estimator that builds on our previous work with diffuse scattering in layered media. We first characterize the performance of our sound speed estimator and distributed aberration correction techniques in simulations where the scattering in the media is known a priori. Phantom and in vivo experiments further demonstrate the capabilities of the sound speed estimator and the aberration correction techniques. In phantom experiments, point target resolution improves from 0.58 to 0.26 and 0.27 mm, and lesion contrast improves from 17.7 to 23.5 and 25.9 dB, as a result of distributed aberration correction using the eikonal and wavefield correlation techniques, respectively.

Ultrasound Lesion Detectability as a Distance Between Probability Measures.

Lesion detectability (LD) quantifies how easily a lesion or target can be distinguished from the background. LD is commonly used to assess the performance of new ultrasound imaging methods. The contrast-to-noise ratio (CNR) is the most popular measure of LD; however, recent work has exposed its vulnerability to manipulations of dynamic range. The generalized CNR (gCNR) has been proposed as a robust histogram-based alternative that is invariant to such manipulations. Here, we identify key shortcomings of CNR and strengths of gCNR as LD metrics for modern beamformers. Using the measure theory, we pose LD as a distance between empirical probability measures (i.e., histograms) and prove that: 1) gCNR is equal to the total variation distance between probability measures and 2) gCNR is one minus the error rate of the ideal observer. We then explore several consequences of measure-theoretic LD in simulation studies. We find that histogram distances depend on bin selection that LD must be considered in the context of spatial resolution and that many histogram distances are invariant under measure-preserving isomorphisms of the sample space (e.g., dynamic range transformations). Finally, we provide a mathematical interpretation for why quantitative values such as contrast ratio (CR), CNR, and signal-to-noise ratio should not be compared between images with different dynamic ranges or underlying units and demonstrate how histogram matching can be used to reenable such quantitative comparisons.

Upstream Machine Learning in Radiology.

Machine learning (ML) and Artificial intelligence (AI) has the potential to dramatically improve radiology practice at multiple stages of the imaging pipeline. Most of the attention has been garnered by applications focused on improving the end of the pipeline: image interpretation. However, this article reviews how AI/ML can be applied to improve upstream components of the imaging pipeline, including exam modality selection, hardware design, exam protocol selection, data acquisition, image reconstruction, and image processing. A breadth of applications and their potential for impact is shown across multiple imaging modalities, including ultrasound, computed tomography, and MRI.

Deep Learning for Ultrasound Image Formation: CUBDL Evaluation Framework and Open Datasets.

Deep learning for ultrasound image formation is rapidly garnering research support and attention, quickly rising as the latest frontier in ultrasound image formation, with much promise to balance both image quality and display speed. Despite this promise, one challenge with identifying optimal solutions is the absence of unified evaluation methods and datasets that are not specific to a single research group. This article introduces the largest known international database of ultrasound channel data and describes the associated evaluation methods that were initially developed for the challenge on ultrasound beamforming with deep learning (CUBDL), which was offered as a component of the 2020 IEEE International Ultrasonics Symposium. We summarize the challenge results and present qualitative and quantitative assessments using both the initially closed CUBDL evaluation test dataset (which was crowd-sourced from multiple groups around the world) and additional in vivo breast ultrasound data contributed after the challenge was completed. As an example quantitative assessment, single plane wave images from the CUBDL Task 1 dataset produced a mean generalized contrast-to-noise ratio (gCNR) of 0.67 and a mean lateral resolution of 0.42 mm when formed with delay-and-sum beamforming, compared with a mean gCNR as high as 0.81 and a mean lateral resolution as low as 0.32 mm when formed with networks submitted by the challenge winners. We also describe contributed CUBDL data that may be used for training of future networks. The compiled database includes a total of 576 image acquisition sequences. We additionally introduce a neural-network-based global sound speed estimator implementation that was necessary to fairly evaluate the results obtained with this international database. The integration of CUBDL evaluation methods, evaluation code, network weights from the challenge winners, and all datasets described herein are publicly available (visit https://cubdl.jhu.edu for details).

Real-Time In Vivo Imaging of Human Liver Vasculature Using Coherent Flow Power Doppler: A Pilot Clinical Study.

Power Doppler (PD) is a commonly used technique for flow detection and vessel visualization in radiology clinics. Despite its broad set of applications, PD suffers from multiple noise sources and artifacts, such as thermal noise, clutter, and flash artifacts. In addition, a tradeoff exists between acquisition time and Doppler image quality. These limit the ability of clinical PD imaging in deep-lying and small-vessel detection and visualization, particularly among patients with high body mass indices (BMIs). To improve the Doppler vessel detection, we have previously proposed coherent flow PD (CFPD) imaging and demonstrated its performance on porcine vasculature. In this article, we report on a pilot clinical study of CFPD imaging on healthy human volunteers and patients with high BMI to assess the clinical feasibility of the technique in liver imaging. In this study, we built a real-time CFPD imaging system using a graphical processing unit (GPU)-based software beamformer and a CFPD processing module. Using the real-time CFPD imaging system, the liver vasculature of 15 healthy volunteers with normal BMI below 25 and 15 patients with BMI greater than 25 was imaged. Both PD and CFPD image streams were produced simultaneously. The generalized contrast-to-noise ratio (gCNR) of the PD and CFPD images was measured to provide the quantitative evaluation of image quality and vessel detectability. Comparison of PD and CFPD image shows that gCNR is improved by 35% in healthy volunteers and 28% in high BMI patients with CFPD compared to PD. Example images are provided to show that the improvement in the Doppler image gCNR leads to greater detection of small vessels in the liver. In addition, we show that CFPD can suppress in vivo reverberation clutter in clinical imaging.

Superiorized Photo-Acoustic Non-NEgative Reconstruction (SPANNER) for Clinical Photoacoustic Imaging.

Photoacoustic (PA) imaging can revolutionize medical ultrasound by augmenting it with molecular information. However, clinical translation of PA imaging remains a challenge due to the limited viewing angles and imaging depth. Described here is a new robust algorithm called Superiorized Photo-Acoustic Non-NEgative Reconstruction (SPANNER), designed to reconstruct PA images in real-time and to address the artifacts associated with limited viewing angles and imaging depth. The method utilizes precise forward modeling of the PA propagation and reception of signals while accounting for the effects of acoustic absorption, element size, shape, and sensitivity, as well as the transducer's impulse response and directivity pattern. A fast superiorized conjugate gradient algorithm is used for inversion. SPANNER is compared to three reconstruction algorithms: delay-and-sum (DAS), universal back-projection (UBP), and model-based reconstruction (MBR). All four algorithms are applied to both simulations and experimental data acquired from tissue-mimicking phantoms, ex vivo tissue samples, and in vivo imaging of the prostates in patients. Simulations and phantom experiments highlight the ability of SPANNER to improve contrast to background ratio by up to 20 dB compared to all other algorithms, as well as a 3-fold increase in axial resolution compared to DAS and UBP. Applying SPANNER on contrast-enhanced PA images acquired from prostate cancer patients yielded a statistically significant difference before and after contrast agent administration, while the other three image reconstruction methods did not, thus highlighting SPANNER's performance in differentiating intrinsic from extrinsic PA signals and its ability to quantify PA signals from the contrast agent more accurately.

Reverberation Noise Suppression in Ultrasound Channel Signals Using a 3D Fully Convolutional Neural Network.

Diffuse reverberation is ultrasound image noise caused by multiple reflections of the transmitted pulse before returning to the transducer, which degrades image quality and impedes the estimation of displacement or flow in techniques such as elastography and Doppler imaging. Diffuse reverberation appears as spatially incoherent noise in the channel signals, where it also degrades the performance of adaptive beamforming methods, sound speed estimation, and methods that require measurements from channel signals. In this paper, we propose a custom 3D fully convolutional neural network (3DCNN) to reduce diffuse reverberation noise in the channel signals. The 3DCNN was trained with channel signals from simulations of random targets that include models of reverberation and thermal noise. It was then evaluated both on phantom and in-vivo experimental data. The 3DCNN showed improvements in image quality metrics such as generalized contrast to noise ratio (GCNR), lag one coherence (LOC) contrast-to-noise ratio (CNR) and contrast for anechoic regions in both phantom and in-vivo experiments. Visually, the contrast of anechoic regions was greatly improved. The CNR was improved in some cases, however the 3DCNN appears to strongly remove uncorrelated and low amplitude signal. In images of in-vivo carotid artery and thyroid, the 3DCNN was compared to short-lag spatial coherence (SLSC) imaging and spatial prediction filtering (FXPF) and demonstrated improved contrast, GCNR, and LOC, while FXPF only improved contrast and SLSC only improved CNR.

Histogram Matching for Visual Ultrasound Image Comparison.

The widespread development of new ultrasound image formation techniques has created a need for a standardized methodology for comparing the resulting images. Traditional methods of evaluation use quantitative metrics to assess the imaging performance in specific tasks, such as point resolution or lesion detection. Quantitative evaluation is complicated by unconventional new methods and nonlinear transformations of the dynamic range of data and images. Transformation-independent image metrics have been proposed for quantifying task performance. However, clinical ultrasound still relies heavily on visualization and qualitative assessment by expert observers. We propose the use of histogram matching to better assess differences across image formation methods. We briefly demonstrate the technique using a set of sample beamforming methods and discuss the implications of such image processing. We present variations of histogram matching and provide code to encourage the application of this method within the imaging community.

Passive Cavitation Mapping by Cavitation Source Localization From Aperture-Domain Signals-Part II: Phantom and In Vivo Experiments.

Passive cavitation mapping (PCM) techniques typically utilize a time-exposure acoustic (TEA) approach, where the received radio frequency data are beamformed, squared, and integrated over time. Such PCM-TEA cavitation maps typically suffer from long-tail artifacts and poor axial resolution with pulse-echo diagnostic arrays. Here, we utilize a recently developed PCM technique based on cavitation source localization (CSL), which fits a hyperbolic function to the received cavitation wavefront. A filtering method based on the root-mean-square error (rmse) of the hyperbolic fit is utilized to filter out spurious signals. We apply a wavefront correction technique to the signals with poor fit quality to recover additional cavitation signals and improve cavitation localization. Validation of the PCM-CSL technique with rmse filtering and wavefront correction was conducted in experiments with a tissue-mimicking flow phantom and an in vivo mouse model of cancer. It is shown that the quality of the hyperbolic fit, necessary for the PCM-CSL, requires an rmse < 0.05 mm2 in order to accurately localize the cavitation sources. A detailed study of the wavefront correction technique was carried out, and it was shown that, when applied to experiments with high noise and interference from multiple cavitating microbubbles, it was capable of effectively correcting noisy wavefronts without introducing spurious cavitation sources, thereby improving the quality of the PCM-CSL images. In phantom experiments, the PCM-CSL was capable of precisely localizing sources on the therapy beam axis and off-axis sources. In vivo cavitation experiments showed that PMC-CSL showed a significant improvement over PCM-TEA and yielded acceptable localization of cavitation signals in mice.

Blood Flow Imaging in the Neonatal Brain Using Angular Coherence Power Doppler.

Using ultrasound to image small vessels in the neonatal brain can be difficult in the presence of strong clutter from the surrounding tissue and with a neonate motion during the scan. We propose a coherence-based beamforming method, namely the short-lag angular coherence (SLAC) beamforming that suppresses incoherent noise and motion artifacts in Ultrafast data, and we demonstrate its applicability to improve detection of blood flow in the neonatal brain. Instead of estimating spatial coherence across the receive elements, SLAC utilizes the principle of acoustic reciprocity to estimate angular coherence from the beamsummed signals from different plane-wave transmits, which makes it computationally efficient and amenable to advanced beamforming techniques, such as f-k migration. The SLAC images of a simulated speckle phantom show similar edge resolution and texture size as the matching B-mode images, and reduced random noise in the background. We apply SLAC power Doppler (PD) to free-hand imaging of neonatal brain vasculature with long Doppler ensembles and show that: 1) it improves visualization of small vessels in the cortex compared to conventional PD and 2) it can be used for tracking of blood flow in the brain over time, meaning it could potentially improve the quality of free-hand functional ultrasound.

Nondestructive Detection of Targeted Microbubbles Using Dual-Mode Data and Deep Learning for Real-Time Ultrasound Molecular Imaging.

Ultrasound molecular imaging (UMI) is enabled by targeted microbubbles (MBs), which are highly reflective ultrasound contrast agents that bind to specific biomarkers. Distinguishing between adherent MBs and background signals can be challenging in vivo. The preferred preclinical technique is differential targeted enhancement (DTE), wherein a strong acoustic pulse is used to destroy MBs to verify their locations. However, DTE intrinsically cannot be used for real-time imaging and may cause undesirable bioeffects. In this work, we propose a simple 4-layer convolutional neural network to nondestructively detect adherent MB signatures. We investigated several types of input data to the network: "anatomy-mode" (fundamental frequency), "contrast-mode" (pulse-inversion harmonic frequency), or both, i.e., "dual-mode", using IQ channel signals, the channel sum, or the channel sum magnitude. Training and evaluation were performed on in vivo mouse tumor data and microvessel phantoms. The dual-mode channel signals yielded optimal performance, achieving a soft Dice coefficient of 0.45 and AUC of 0.91 in two test images. In a volumetric acquisition, the network best detected a breast cancer tumor, resulting in a generalized contrast-to-noise ratio (GCNR) of 0.93 and Kolmogorov-Smirnov statistic (KSS) of 0.86, outperforming both regular contrast mode imaging (GCNR = 0.76, KSS = 0.53) and DTE imaging (GCNR = 0.81, KSS = 0.62). Further development of the methodology is necessary to distinguish free from adherent MBs. These results demonstrate that neural networks can be trained to detect targeted MBs with DTE-like quality using nondestructive dual-mode data, and can be used to facilitate the safe and real-time translation of UMI to clinical applications.

Effects of motion on correlations of pulse-echo ultrasound signals: Applications in delay estimation and aperture coherence.

The correlation between two pulse-echo ultrasound signals is used to achieve a wide range of ultrasound techniques, such as Doppler imaging and elastography. Prior theoretical descriptions of pulse-echo correlations were restricted to stationary scatterers. Here, a theory for the correlation of moving scatterers is presented. An expression is derived for the correlation of two pulse-echo signals with arbitrary transmit and receive apertures acquired from a medium undergoing bulk motion using the Fresnel approximation. The derivation is shown to coincide with prior derivations in the absence of scatterer motion. The theory was compared against simulations in applications of phase-shift estimation and aperture coherence measurements. The phase-shift estimate and jitter were accurately predicted under axial and transverse motion for focused transmit apertures and for sequential and interleaved synthetic transmit apertures. The theory also accurately predicted how motion affects the correlation coefficient between receive aperture elements for a synthetic transmit aperture. The presented theory provides a framework for analyzing the correlations of arbitrary pulse-echo configurations for applications in which scatterer motion is expected.

Acoustically Driven Microbubbles Enable Targeted Delivery of microRNA-Loaded Nanoparticles to Spontaneous Hepatocellular Neoplasia in Canines.

Spatially localized microbubble cavitation by ultrasound offers an effective means of altering permeability of natural barriers (i.e. blood vessel and cell membrane) in favor of nanomaterials accumulation in the target site. In this study, a clinically relevant, minimally invasive ultrasound guided therapeutic approach is investigated for targeted delivery of anticancer microRNA loaded PLGA-b-PEG nanoparticles to spontaneous hepatocellular neoplasia in a canine model. Quantitative assessment of the delivered microRNAs revealed prominent and consistent increase in miRNAs levels (1.5-to 2.3-fold increase (p<0.001)) in ultrasound treated tumor regions compared to untreated control regions. Immunohistology of ultrasound treated tumor tissue presented a clear evidence for higher amount of nanoparticles extravasation from the blood vessels. A distinct pattern of cytokine expression supporting CD8+ T cells mediated "cold-to-hot" tumor transition was evident in all patients. On the outset, proposed platform can enhance delivery of miRNA-loaded nanoparticles to deep seated tumors in large animals to enhance chemotherapy.

Extending Retrospective Encoding for Robust Recovery of the Multistatic Data Set.

Robust recovery of multistatic synthetic aperture data from conventional ultrasound sequences can enable complete transmit-and-receive focusing at all points in the field of view without the drawbacks of virtual-source synthetic aperture and further enables more advanced imaging applications, such as backscatter coherence, sound speed estimation, and phase aberration correction. Recovery of the multistatic data set has previously been demonstrated on a steered transmit sequence for phased arrays using an adjoint-based method. We introduce two methods to improve the accuracy of the multistatic data set. We first modify the original technique used for steered transmit sequences by applying a ramp filter to compensate for the nonuniform frequency scaling introduced by the adjoint-based method. Then, we present a regularized inversion technique that allows additional aperture specification and is intended to work for both steered transmit and walking aperture sequences. The ramp-filtered adjoint and regularized inversion techniques, respectively, improve the correlation of the recovered signal with the ground truth from 0.9404 to 0.9774 and 0.9894 in steered transmit sequences and 0.4610 to 0.4733 and 0.9936 in walking aperture sequences.

Beamforming and Speckle Reduction Using Neural Networks.

With traditional beamforming methods, ultrasound B-mode images contain speckle noise caused by the random interference of subresolution scatterers. In this paper, we present a framework for using neural networks to beamform ultrasound channel signals into speckle-reduced B-mode images. We introduce log-domain normalization-independent loss functions that are appropriate for ultrasound imaging. A fully convolutional neural network was trained with the simulated channel signals that were coregistered spatially to ground-truth maps of echogenicity. Networks were designed to accept 16 beamformed subaperture radio frequency (RF) signals. Training performance was compared as a function of training objective, network depth, and network width. The networks were then evaluated on the simulation, phantom, and in vivo data and compared against the existing speckle reduction techniques. The most effective configuration was found to be the deepest (16 layer) and widest (32 filter) networks, trained to minimize a normalization-independent mixture of the l1 and multiscale structural similarity (MS-SSIM) losses. The neural network significantly outperformed delay-and-sum (DAS) and receive-only spatial compounding in speckle reduction while preserving resolution and exhibited improved detail preservation over a nonlocal means method. This work demonstrates that ultrasound B-mode image reconstruction using machine-learned neural networks is feasible and establishes that networks trained solely in silico can be generalized to real-world imaging in vivo to produce images with significantly reduced speckle.

Short-lag Spatial Coherence Imaging in 1.5-D and 1.75-D Arrays: Elevation Performance and Array Design Considerations.

Short-lag spatial coherence (SLSC) imaging has demonstrated improved performance over conventional B-Mode ultrasound imaging. Previous work has evaluated the performance of SLSC using 2-D matrix arrays in simulation and in vivo studies across various levels of subaperture beamforming, demonstrating improved contrast-to-noise ratio (CNR) and speckle signal-to-noise ratio (SNR) over 1-D arrays. This work explores the application of SLSC imaging in 1.5-D and 1.75-D arrays to quantify the impacts of elevation element count, mirroring, and Fresnel element spacing on SLSC image quality. Through simulation and in vivo studies, increased elevation element count was shown to improve CNR and speckle SNR relative to 1-D SLSC and B-Mode images. Elevation mirroring (1.5-D) was shown to force the inclusion of long lags into the SLSC calculation, introducing additional decorrelation and reducing image quality relative to 1.75-D arrays with individually-connected elements. These results demonstrate the effectiveness of SLSC imaging in 1.5-D and 1.75-D arrays.

Improved Visualization in Difficult-to-Image Stress Echocardiography Patients Using Real-Time Harmonic Spatial Coherence Imaging.

Stress echocardiography is used to detect myocardial ischemia by evaluating cardiovascular function both at rest and at elevated heart rates. Stress echocardiography requires excellent visualization of the left ventricle (LV) throughout the cardiac cycle. However, LV endocardial border visualization is often negatively impacted by high levels of clutter associated with patient obesity, which has risen dramatically worldwide in recent decades. Short-lag spatial coherence (SLSC) imaging has demonstrated reduced clutter in several applications. In this work, a computationally efficient formulation of SLSC was implemented into an object-oriented graphics processing unit-based software beamformer, enabling real-time (>30 frames per second) SLSC echocardiography on a research ultrasound scanner. The system was then used to image 15 difficult-to-image stress echocardiography patients in a comparison study of tissue harmonic imaging (THI) and harmonic spatial coherence imaging (HSCI). Video clips of four standard stress echocardiography views acquired with either THI or HSCI were provided in random shuffled order to three experienced readers. Each reader rated the visibility of 17 LV segments as "invisible," "suboptimally visualized," or "well visualized," with the first two categories indicating a need for contrast agent. In a symmetry test unadjusted for patientwise clustering, HSCI demonstrated a clear superiority over THI ( ). When measured on a per-patient basis, the median total score significantly favored HSCI with . When collapsing the ratings to a two-level scale ("needs contrast" versus "well visualized"), HSCI once again showed an overall superiority over THI, with by McNemar test adjusted for clustering.

Local speed of sound estimation in tissue using pulse-echo ultrasound: Model-based approach.

A model and method to accurately estimate the local speed of sound in tissue from pulse-echo ultrasound data is presented. The model relates the local speeds of sound along a wave propagation path to the average speed of sound over the path, and allows one to avoid bias in the sound-speed estimates that can result from overlying layers of subcutaneous fat and muscle tissue. Herein, the average speed of sound using the approach by Anderson and Trahey is measured, and then the authors solve the proposed model for the local sound-speed via gradient descent. The sound-speed estimator was tested in a series of simulation and ex vivo phantom experiments using two-layer media as a simple model of abdominal tissue. The bias of the local sound-speed estimates from the bottom layers is less than 6.2 m/s, while the bias of the matched Anderson's estimates is as high as 66 m/s. The local speed-of-sound estimates have higher standard deviation than the Anderson's estimates. When the mean local estimate is computed over a 5-by-5 mm region of interest, its standard deviation is reduced to less than 7 m/s.