Phase aberration correction using near-field signal redundancy. I. Principles [Ultrasound medical imaging]

Investigation of a method to estimate the average speed of sound using phase variances of element signals for ultrasound compound imaging

PURPOSE

In the receive beamforming of an ultrasonography system, a B-mode image is reconstructed by assuming an average speed of sound (SoS) as a constant value. In our previous studies, we proposed a method for estimating the average SoS based on the coherence factor (CF) and the reciprocal of phase variances of element signals in delay-and-sum (DAS) beamforming. In this paper, we investigate the accuracy of estimation of the average SoS for compound imaging.

METHODS

For this purpose, two numerical simulations were performed with k-Wave software. Also, the estimation methods based on the CF and the reciprocal were applied to in vivo data from the common carotid artery, and B-mode images were reconstructed using the estimated average SoS.

RESULTS

In the first numerical simulation using an inhomogeneous phantom, the relationship between the accuracy and the transmission angles for the estimation was investigated, and the root mean squared errors (RMSEs) of estimates obtained based on the CF and the reciprocal of the phase variance were 1.25 ± 0.09, and 0.765 ± 0.17% at the transmission sequence of steering angles of (- 10°, - 5°, 0°, 5°, 10°), respectively. In the second numerical simulation using a cyst phantom, lateral resolutions were improved by reconstructing the image using the estimates obtained using the proposed strategy (reciprocal). By the proposed strategy, improvement of the continuity of the lumen-intima interface in the lateral direction was observed in the in vivo experiment.

CONCLUSION

Consequently, the results indicated that the proposed strategy was beneficial for estimation of the average SoS and image reconstruction.

Aberration correction in diagnostic ultrasound: A review of the prior field and current directions

Medical ultrasound images are reconstructed with simplifying assumptions on wave propagation, with one of the most prominent assumptions being that the imaging medium is composed of a constant sound speed. When the assumption of a constant sound speed are violated, which is true in most in vivoor clinical imaging scenarios, distortion of the transmitted and received ultrasound wavefronts appear and degrade the image quality. This distortion is known as aberration, and the techniques used to correct for the distortion are known as aberration correction techniques. Several models have been proposed to understand and correct for aberration. In this review paper, aberration and aberration correction are explored from the early models and correction techniques, including the near-field phase screen model and its associated correction techniques such as nearest-neighbor cross-correlation, to more recent models and correction techniques that incorporate spatially varying aberration and diffractive effects, such as models and techniques that rely on the estimation of the sound speed distribution in the imaging medium. In addition to historical models, future directions of ultrasound aberration correction are proposed.

Improved forward model for quantitative pulse-echo speed-of-sound imaging

Computed ultrasound tomography in echo mode (CUTE) allows determining the spatial distribution of speed-of-sound (SoS) inside tissue using handheld pulse-echo ultrasound (US). This technique is based on measuring the changing phase of beamformed echoes obtained under varying transmit (Tx) and/or receive (Rx) steering angles. The SoS is reconstructed by inverting a forward model describing how the spatial distribution of SoS is related to the spatial distribution of the echo phase shift. Thanks to the straight-ray approximation, this forward model is linear and can be inverted in real-time when implemented in a state-of-the art system. Here we demonstrate that the forward model must contain two features that were not taken into account so far: (a) the phase shift must be detected between pairs of Tx and Rx angles that are centred around a set of common mid-angles, and (b) it must account for an additional phase shift induced by the offset of the reconstructed position of echoes. In a phantom study mimicking hepatic and cancer imaging, we show that both features are required to accurately predict echo phase shift among different phantom geometries, and that substantially improved quantitative SoS images are obtained compared to the model that has been used so far. The importance of the new model is corroborated by a preliminary volunteer result.

Using redundancy of round-trip ultrasound signal for non-continuous arrays: Application to gap and blockage compensation

In ultrasound imaging, an array of elements is used to image a medium. If part of the array is blocked by an obstacle, or if the array is made from several sub-arrays separated by a gap, grating lobes appear and the image is degraded. The grating lobes are caused by missing spatial frequencies, corresponding to the blocked or non-existing elements. However, in an active imaging system, where elements are used both for transmitting and receiving, the round trip signal is redundant: different pairs of transmit and receive elements carry similar information. It is shown here that, if the gaps are smaller than the active sub-apertures, this redundancy can be used to compensate for the missing signals and recover full resolution. Three algorithms are proposed: one is based on a synthetic aperture method, a second one uses dual-apodization beamforming, and the third one is a radio frequency (RF) data based deconvolution. The algorithms are evaluated on simulated and experimental data sets. An application could be imaging through ribs with a large aperture.

An Ultrasonic-Adaptive Beamforming Method and Its Application for Trans-skull Imaging of Certain Types of Head Injuries; Part I: Transmission Mode

A new adaptive beamforming algorithm for imaging via small-aperture 1-D ultrasonic-phased arrays through composite layered structures is reported. Such structures cause acoustic phase aberration and wave refraction at undulating interfaces and can lead to significant distortion of an ultrasonic field pattern produced by conventional beamforming techniques. This distortion takes the form of defocusing the ultrasonic field transmitted through the barrier and causes loss of resolution and overall degradation of image quality. To compensate for the phase aberration and the refractional effects, we developed and examined an adaptive beamforming algorithm for small-aperture linear-phased arrays. After accurately assessing the barrier's local geometry and sound speed, the method calculates a new timing scheme to refocus the distorted beam at its original location. As a tentative application, implementation of this method for trans-skull imaging of certain types of head injuries through human skull is discussed. Simulation and laboratory results of applying the method on skull-mimicking phantoms are presented. Correction of up to 2.5 cm focal point displacement at up to 10 cm depth under our skull phantom is demonstrated. Quantitative assessment of the method in a variety of temporal focusing scenarios is also reported. Overall temporal deviation on the order of a few nanoseconds was observed between the simulated and experimental results. The single-point adaptive focusing results demonstrate strong potential of our approach for diagnostic imaging through intact human skull. The algorithms were implemented on an ultrasound advanced open-platform controlling 64 active elements on a 128-element phased array.

Timing-error-difference calibration of a two-dimensional array imaging system using the overlapping-subaperture algorithm

Timing errors in the transmitting and receiving electronic channels of an imaging system can generate different transmission and reception phase-aberration profiles. To decide if these two profiles need to be measured separately, an overlapping-subaperture algorithm has been proposed in a previous paper to measure the difference between timing errors in transmitting and receiving channels connected to each element in a two-dimensional array. This algorithm has been used to calibrate a custom built imaging system with a curved linear two-dimensional array, and the results are presented in this paper. The experimental results have demonstrated that the overlapping-subaperture algorithm is capable of calibrating the timing-error-difference profile of this imaging system with a standard deviation of only a few nanoseconds. Experimental results have also shown that the time-error-difference profile of this imaging system is smaller than one tenth of a wavelength and there is no need to measure the transmission and reception phase-aberration profiles separately. The derived average phase-aberration profile using the near-field signal-redundancy algorithm can be used to correct phase aberrations for both transmission and reception.

Correction of tissue-motion effects on common-midpoint signals using reciprocal signals

The near field signal redundancy algorithm for phase-aberration correction is sensitive to tissue motion because several separated transmissions are usually needed to acquire a set of common-midpoint signals. If tissues are moving significantly due to, for example, heart beats, the effects of tissue motion on common-midpoint signals need to be corrected before the phase-aberration profile can be successfully measured. Theoretical analyses in this paper show that the arrival-time difference between a pair of common-midpoint signals due to tissue motion is usually very similar to that between the pair of reciprocal signals acquired using the same two transmissions. Based on this conclusion, an algorithm for correcting tissue-motion effects on the peak position of cross-correlation functions between common-midpoint signals is proposed and initial experimental results are also presented.

High-frame-rate echocardiography using diverging transmit beams and parallel receive beamforming

PURPOSE

Echocardiography is a widely used modality for diagnosis of the heart. It enables observation of the shape of the heart and estimation of global heart function based on B-mode and M-mode imaging. Subsequently, methods for estimating myocardial strain and strain rate have been developed to evaluate regional heart function. Furthermore, it has recently been shown that measurements of transmural transition of myocardial contraction/relaxation and propagation of vibration caused by closure of a heart valve would be useful for evaluation of myocardial function and viscoelasticity. However, such measurements require a frame rate much higher than that achieved by conventional ultrasonic diagnostic equipment. In the present study, a method based on parallel receive beamforming was developed to achieve high-frame-rate (over 300 Hz) echocardiography.

METHODS

To increase the frame rate, the number of transmits was reduced to 15 with angular intervals of 6°, and 16 receiving beams were created for each transmission to obtain the same number and density of scan lines as realized by conventional sector scanning. In addition, several transmits were compounded to obtain each scan line to reduce the differences in transmit-receive sensitivities among scan lines. The number of transmits for compounding was determined by considering the width of the transmit beam. For transmission, plane waves and diverging waves were investigated. Diverging waves showed better performance than plane waves because the widths of plane waves did not increase with the range distance from the ultrasonic probe, whereas lateral intervals of scan lines increased with range distance.

RESULTS

The spatial resolution of the proposed method was validated using fine nylon wires. Although the widths at half-maxima of the point spread functions obtained by diverging waves were slightly larger than those obtained by conventional beamforming and parallel beamforming with plane waves, point spread functions very similar to those obtained by conventional beamforming could be realized by parallel beamforming with diverging beams and compounding. However, there was an increase in the lateral sidelobe level in the case of parallel beamforming with plane and diverging waves. Furthermore, the heart of a 23-year-old healthy male was measured.

CONCLUSION

Although the contrast of the B-mode image obtained by the proposed method was degraded due to the increased sidelobe level, a frame rate of 316 Hz, much higher than that realized by conventional sector scanning of several tens of Hertz, was realized with a full lateral field of view of 90°.

A model of distributed phase aberration for deblurring phase estimated from scattering

Correction of aberration in ultrasound imaging uses the response of a point reflector or its equivalent to characterize the aberration. Because a point reflector is usually unavailable, its equivalent is obtained using statistical methods, such as processing reflections from multiple focal regions in a random medium. However, the validity of methods that use reflections from multiple points is limited to isoplanatic patches for which the aberration is essentially the same. In this study, aberration is modeled by an offset phase screen to relax the isoplanatic restriction. Methods are developed to determine the depth and phase of the screen and to use the model for compensation of aberration as the beam is steered. Use of the model to enhance the performance of the noted statistical estimation procedure is also described. Experimental results obtained with tissue-mimicking phantoms that implement different models and produce different amounts of aberration are presented to show the efficacy of these methods. The improvement in b-scan resolution realized with the model is illustrated. The results show that the isoplanatic patch assumption for estimation of aberration can be relaxed and that propagation-path characteristics and aberration estimation are closely related.

Evaluating the robustness of dual apodization with cross-correlation

We have recently presented a new method to suppress side lobes and clutter in ultrasound imaging called dual apodization with cross-correlation (DAX). However, due to the random nature of speckle, artifactual black spots may arise with DAX-processed images. In this paper, we present one possible solution, called dynamic DAX, to reduce these black spots. We also evaluate the robustness of dynamic DAX in the presence of phase aberration and noise. Simulation results using a 5 MHz, 128-element linear array are presented using dynamic DAX with aberrator strengths ranging from 25 ns root-mean-square (RMS) to 45 ns RMS and correlation lengths of 3 mm and 5 mm. When simulating a 3 mm diameter anechoic cyst, at least 100% improvement in the contrast-to-noise ratio (CNR) compared with standard beamforming is seen using dynamic DAX, except in the most severe case. Layers of pig skin, fat, and muscle were used as experimental aberrators. Simulation and experimental results are also presented using dynamic DAX in the presence of noise. With a system signal-to-noise ratio (SNR) of at least 15 dB, we have a CNR improvement of more than 100% compared with standard beamforming. This work shows that dynamic DAX is able to improve the contrast-to-noise ratio reliably in the presence of phase aberration and noise.

Timing-error-difference calibration using reciprocal signals

Timing errors in transmission and reception electronic channels of medical ultrasound imaging systems are generally smaller than one-tenth of a wavelength and do not influence the focusing quality of the system. However, these errors influence the performance of the near-field-signal-redundancy algorithm for correcting phase-aberrations generated by speed heterogeneity in the medium due to its high sensitivity to errors. The effect of timing errors is to make the transmission and reception phase-aberration profiles different. When the difference is much smaller than the period of the signal, an algorithm has been proposed in a previous work to measure the average of the transmission and reception phase-aberration profiles, and it can be used as an approximation to correct phase-aberrations on both transmission and reception. However, when the difference is large, the transmission and reception phase-aberration profiles need to be measured separately. In this paper, several algorithms that use reciprocal signals are proposed to measure the difference profile of the transmission and reception phase-aberration profiles. Their performances are theoretically analyzed, simulated, and experimentally tested. From the measured average and difference profiles, the transmission and reception phase-aberration profiles can be derived separately and used to correct phase-aberrations on transmission and reception, respectively.

Sidelobe suppression in ultrasound imaging using dual apodization with cross-correlation

This paper introduces a novel sidelobe and clutter suppression method in ultrasound imaging called dual apodization with cross-correlation or DAX. DAX dramatically improves the contrast-to-noise ratio (CNR) allowing for easier visualization of anechoic cysts and blood vessels. This technique uses dual apodization or weighting strategies that are effective in removing or minimizing clutter and efficient in terms of computational load and hardware/software needs. This dual apodization allows us to determine the amount of mainlobe versus clutter contribution in a signal by cross-correlating RF data acquired from 2 apodization functions. Simulation results using a 128 element 5 MHz linear array show an improvement in CNR of 139% compared with standard beamformed data with uniform apodization in a 3 mm diameter anechoic cylindrical cyst. Experimental CNR using a tissue-mimicking phantom with the same sized cyst shows an improvement of 123% in a DAX processed image.

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.

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.

Wavelet restoration of medical pulse-echo ultrasound images in an EM framework

The clinical utility of pulse-echo ultrasound images is severely limited by inherent poor resolution that impacts negatively on their diagnostic potential. Research into the enhancement of image quality has mostly been concentrated in the areas of blind image restoration and speckle removal, with little regard for accurate modeling of the underlying tissue reflectivity that is imaged. The acoustic response of soft biological tissues has statistics that differ substantially from the natural images considered in mainstream image processing: although, on a macroscopic scale, the overall tissue echogenicity does behave some-what like a natural image and varies piecewise-smoothly, on a microscopic scale, the tissue reflectivity exhibits a pseudo-random texture (manifested in the amplitude image as speckle) due to the dense concentrations of small, weakly scattering particles. Recognizing that this pseudorandom texture is diagnostically important for tissue identification, we propose modeling tissue reflectivity as the product of a piecewise-smooth echogenicity map and a field of uncorrelated, identically distributed random variables. We demonstrate how this model of tissue reflectivity can be exploited in an expectation-maximization (EM) algorithm that simultaneously solves the image restoration problem and the speckle removal problem by iteratively alternating between Wiener filtering (to solve for the tissue reflectivity) and wavelet-based denoising (to solve for the echogenicity map). Our simulation and in vitro results indicate that our EM algorithm is capable of producing restored images that have better image quality and greater fidelity to the true tissue reflectivity than other restoration techniques based on simpler regularizing constraints.

Implementation of the near-field signal redundancy phase-aberration correction algorithm on two-dimensional arrays

Near-field signal-redundancy (NFSR) algorithms for phase-aberration correction have been proposed and experimentally tested for linear and phased one-dimensional arrays. In this paper the performance of an all-row-plus-two-column, two-dimensional algorithm has been analyzed and tested with simulated data sets. This algorithm applies the NFSR algorithm for one-dimensional arrays to all the rows as well as the first and last columns of the array. The results from the two column measurements are used to derive a linear term for each row measurement result. These linear terms then are incorporated into the row results to obtain a two-dimensional phase aberration profile. The ambiguity phase aberration profile, which is the difference between the true and the derived phase aberration profiles, of this algorithm is not linear. Two methods, a trial-and-error method and a diagonal-measurement method, are proposed to linearize the ambiguity profile. The performance of these algorithms is analyzed and tested with simulated data sets.

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.

Position and time-delay calibration of transducer elements in a sparse array for underwater ultrasound imaging

This paper describes a novel method for the calibration of the position and time delay of transducer elements in a large, sparse array used for underwater, high-resolution ultrasound imaging. This method is based on the principles used in the global positioning system (GPS). However, unlike GPS, in which the wave propagation speed is generally assumed known, the sound propagation speed in the water usually is unknown and it is calibrated simultaneously in this method to achieve high calibration accuracy. In this method, a high-precision positioning system is used to scan a single hydrophone (used for transmission) in the imaging field of the array. The hydrophone transmits pulses at selected positions, and the transducer elements in the sparse array receive the transmitted signals. Time of flight (TOF) values between transducer elements and hydrophone positions then are measured. From a series of measured TOF values, the position and time delay values for each transducer element as well as the propagation speed can be calibrated. The performances of the calibration algorithm are theoretically analyzed and evaluated with numerical calculations and simulation studies. It is found that this method is capable of calibrating the positions and time delays of transducer elements with high accuracy.

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.

Spatial and temporal aberrator stability for real-time adaptive imaging

Reported real-time adaptive imaging systems use near-field phase correction techniques, which are desired because of their simple implementation and their compatibility with current system architectures. Aberrator stability is important to adaptive imaging because it defines the spatial and temporal limits for which the near-field phase estimates are valid. Spatial aberrator stability determines the required spatial sampling of the aberrator, and temporal aberrator stability determines the length of time for which the aberration profile can be used. In this study, the spatial and temporal stability of clinically measured aberrations is reported for breast, liver, and thyroid tissue. Cross correlations between aberration estimates revealed aberrators to have azimuthal isoplanatic patch sizes of 0.44, 0.28, and 0.20 mm for breast, liver, and thyroid tissue, respectively, at 80% correlation. Axial isoplanatic patch sizes were 1.26, 0.76, and 1.80 mm for the same tissue, respectively, at 80% correlation. Temporal stability at 80% correlation was determined to be greater than 1.5 seconds for breast and thyroid tissue, and 0.65 seconds for the liver. The effects of noise, motion, and target nonuniformity on aberrator stability are characterized by simulations and experiments in tissue mimicking phantoms.

Adaptive imaging and spatial compounding in the presence of aberration

Spatial compounding reduces speckle and increases image contrast by incoherently averaging images acquired at different viewing angles. Adaptive imaging improves contrast and resolution by compensating for tissue-induced phase errors. Aberrator strength and spatial frequency content markedly impact the desirable operating characteristics and performance of these methods for improving image quality. Adaptive imaging, receive-spatial compounding, and a combination of these two methods are presented in contrast and resolution tasks under various aberration characteristics. All three imaging methods yield increases in the contrast-to-noise ratio (CNR) of anechoic cysts; however, the improvements vary depending on the properties of the aberrating layer. Phase correction restores image spatial frequencies, and the addition of compounding opposes the restoration of image spatial frequencies. Lesion signal-to-noise ratio (SNR), an image quality metric for predicting lesion detectability, shows that combining spatial compounding with phase correction yields the maximum detectability when the aberrator strength or spatial frequency content is high. Examples of these modes are presented in thyroid tissue.

Overdetermined least-squares aberration estimates using common-midpoint signals

As medical ultrasound imaging moves to larger apertures and higher frequencies, tissue sound-speed variations continue to limit resolution. In geophysical imaging, a standard approach for estimating near-surface aberrating delays is to analyze the time shifts between common-midpoint signals. This requires complete data-echoes from every source/receiver pair in the array. Unfocused common-midpoint signals remain highly correlated in the presence of delay aberrations; there is also tremendous redundancy in the data. In medical ultrasound, this technique has been impaired by the wide-angle, random-scattering nature of tissue. This has made it difficult to estimate azimuth-dependent aberration profiles or to harness the full redundancy in the complete data. Prefiltering the data with two-dimensional fan filters mitigates these problems, permitting highly overdetermined, least-squares solutions for the aberration profiles at many steering angles. In experiments with a tissue-mimicking phantom target and silicone rubber aberrators at nonzero stand-off distances from a one-dimensional phased array, this overdetermined, fan-filtering algorithm significantly outperformed other phase-screen algorithms based on nearest-neighbor cross-correlation, speckle brightness maximization, and common-midpoint signal analysis. Our results imply that there is still progress to be made in imaging with single-valued focusing operators. It also appears that the signal-to-noise penalty for using complete data sets is partially compensated by the overdetermined nature of the problem.

Clinical evaluation of combined spatial compounding and adaptive imaging in breast tissue

When spatial compounding is applied to targets with significant acoustic velocity inhomogeneities, the correlation between speckle patterns of the images to be averaged decreases, thereby increasing the speckle reduction nominally obtained. Phase correction applied to these targets improves the coherence of the wavefield and restores image spatial frequencies. Combining these two modes can be used to effectively increase the contrast-to-noise ratio (CNR) of imaging targets and improve the general image quality of these targets over spatial compounding alone. This paper presents a clinical evaluation of combined spatial compounding and adaptive imaging in breast tissue and compares this combined technique to conventional imaging and to adaptive imaging and spatial compounding operating independently. Experiments were performed on a 1.75-D, 8 x 96 array attached to a commercially-available scanner. Cysts, microcalcifications and other breast structures were targeted in order to assess the impact of the combined mode on CNR, target width, target brightness and target peak-to-background ratio (PBR). In general, phase correction improved cyst CNR by 7.7%, decreased target width by 18.7%, increased target brightness by 30.1% and increased PBR by 17.9%. Compounding alone, using three overlapping 9.71 mm subapertures, increased cyst CNR by 24.6%, but increased target width by 25.4% and decreased PBR by 13.2%. Combining both modes, however, increased cyst CNR by 32.6%, inappreciably increased target width by 1.1% and marginally decreased PBR by 2.8%. The increase in target brightness with this combined mode was 20.0%

Spatial coherence of the nonlinearly generated second harmonic portion of backscatter for a clinical imaging system

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter from speckle-producing targets is predicted by the auto correlation of the transmit apodization (Van Cittert-Zernike theorem). Work by others indicates that the second harmonic beam has a wider mainlobe with lower sidelobes than a beam transmitted at 2f. The purpose of this paper is to demonstrate that the spatial coherence of backscatter for the second harmonic is different from that of the fundamental, as would be anticipated from applying the Van Cittert-Zernike theorem to the reported measurements of the second harmonic field. Another objective of this work is to introduce the concept of the effective apodization and to verify that the effective apodization of the second harmonic is narrower than the transmit apodization. The spatial coherence of backscatter was measured using three clinical arrays with a modified clinical imaging system. The spatial coherence results were verified using a pseudo-array scan in a transverse plane of the transmitted field with a hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The spatial coherence for the harmonic portion of backscatter differed systematically and significantly from the auto correlation of the transmit apodization.

Autofocusing in medical ultrasound: the scaled covariance matrix algorithm

This work develops a class of ultrasound phase aberration correction/autofocusing algorithms that are based upon the properties of the covariance matrix of the channel signals for time-delay focused resolution/speckle cells. The scaled covariance matrix (SCM) algorithms are designed to blindly estimate and correct focusing timing errors due to thin layers of unanticipated fatty tissue located in the near field of the transducer array. An important aspect of the algorithm is that the scaling of the covariance matrix elements fundamentally establishes a channel independent phase reference relative to which the aberrant channel phases are estimated. The model development involved the combination of a rigorous mathematical analysis of the scattering of ultrasound in random scattering media and extensive statistical simulation studies with phase aberrations imposed upon both the transmit and received channel signals. Under the assumption of a near field aberration model, the statistical simulation analyses showed that the SCM algorithms in simulation are capable of accurately estimating relative time delay channel errors with rms timing errors up to approximately 62 ns, with interchannel correlation lengths as short as 1.4 mm.

Analysis and correction of ultrasonic wavefront distortion based on a multilayer phase-screen model

A model is introduced that incorporates the cumulative wavefront distortion effects caused by spatial heterogeneities along the path of propagation, and a corresponding model-based wavefront distortion-correction method is presented. In the proposed model, a distributed heterogeneous medium is lumped into a series of parallel phase screens. The distortion effects can be compensated--without a priori knowledge of the distorting structure--by backpropagation of received wavefronts through hypothetical multiple phase screens located between the imaging system and targets, while each pointwise time shift is adjusted iteratively to maximize a specified image quality factor at the final layer. Theoretical analyses indicate that the mean speckle brightness decreases monotonically with the root-mean-square value of distributed phase distortions; therefore, the speckle brightness can be used as an image quality factor. Experimental one-dimensional (1-D) array data with simulated distortion effects based on a real 2-D abdominal-tissue map were used to evaluate the performance of the proposed method and existing aberration-correction techniques. The simulated characteristics of wavefront distortion and relative performance of existing correction techniques were similar to reports based on abdominal-wall data and breast data. This investigation shows that the proposed method provides better compensation for wavefront distortion.

The influences of ambiguity phase aberration profiles on focusing quality in the very near field--part I: single range focusing on transmission

Most phase aberration measurement algorithms have an ambiguity for constant and tilted phase aberration profiles. Based on the Fresnel (near field) approximation with single range focusing and the Fraunhofer (far field) approximation, constant and tilted phase aberration profiles change the position of the focal point only and do not influence the image focusing quality. Therefore, ambiguity phase aberration profiles are generally considered to be harmless and ignored in those algorithms and related theoretical analyses. However, Fresnel and Fraunhofer approximations may become invalid under many medical ultrasound imaging situations, e.g., when the imaging field is in the very near field (f-number approximately 1). In the very near field, although it is known that constant and tilted phase aberration profiles may degrade the focusing quality, it seems that there is a lack of quantitative analysis results in the literature about their influences, and this is the purpose of the current paper. In this paper, a quantitative analysis with a very near field approximation is performed for single range focusing on transmission, which is a commonly used transmission focusing method in medical ultrasound imaging. The tolerable levels of constant and tilted phase aberration profiles are derived as a function of the imaging system's f-number and wavelength. Because some phase aberration measurement algorithms may also have an ambiguity for quadratic phase aberration profiles, they are also included in the analysis. The theoretical results are compared with numerical and simulation results. These results have shown that the influences of tilted and quadratic phase-aberration profiles can be ignored only under certain conditions in the very near field.

The influences of ambiguity phase aberration profiles on focusing quality in the very near field part II: dynamic range focusing on reception

In Part I of this work, the influences of ambiguity phase aberration profiles, including constant, tilted, and quadratic profiles, on focusing quality have been quantitatively analyzed with the very near field approximation for single range focusing on transmission. In this paper, their influences are analyzed in a very different situation: dynamic range focusing on reception, which is commonly used in medical ultrasound imaging for beam formation on reception. It is shown that the results for dynamic range focusing on reception are dramatically different from those for single range focusing on transmission. For example, constant phase aberration profiles are harmless to focusing quality for single range focusing on transmission but become harmful for dynamic range focusing on reception. The analysis also shows that, compared with single range focusing on transmission, dynamic range focusing on reception is much more sensitive to ambiguity phase aberration profiles, which have adverse effects on focusing quality even in the near field and far field. These significant differences are caused by the fundamental differences between single range focusing and dynamic range focusing as well as between transmission and reception. Numerical and simulation results are also derived to test the correctness and accuracy of the theoretical results.

Ultrasound scattering model: 2-D cross-correlation and focusing criteria--theory, simulations, and experiments

A microscopic scattering model is developed to expedite simulation studies of ultrasound imaging in soft tissue using multichannel transducer probes. The model fully accounts for the physics of broadband signals, propagating wave packets, and time delay focusing. Analytical results are presented for 2-D transducer arrays; 1-D results can be trivially extracted by setting the number of rows equal to unity. The 2-D cross-correlation and the 2-D form of the Mallart-Fink (MF) focusing factor are calculated. It is demonstrated that the scattering model reduces to the 2-D form of the monochromatic van Cittert Zernike (VCZ) analysis. Simulation results for the focusing factor are presented, and comparisons are given between the values obtained from simulation, analytical theory, and actual water tank experiments. The comparative results are all in close accord with each other.

Small element array algorithm for correcting phase aberration using near-field signal redundancy. I. Principles

A near-field, signal-redundancy algorithm for measuring phase-aberration profiles has been proposed previously. It is designed for arrays with a relatively large element size for which relatively narrow beams are transmitted and received. The algorithm measures the aberration profile by cross-correlating signals collected with the same midpoint position between transmitter and receiver, termed common midpoint signals, after a dynamic near-field delay correction. In this paper, a near-field signal-redundancy algorithm for small element arrays is proposed. In this algorithm, subarrays are formed of adjacent groups of elements to narrow the beams used to collect common midpoint signals and steer the beam direction, so that angle-dependent, phase-aberration profiles can be measured. There are several methods that could be used to implement the dynamic near-field delay correction on common midpoint signals collected with subarrays. In this paper, the similarity between common midpoint signals collected with these methods is also analyzed and compared using a so-called corresponding-signal concept. This analysis should be valid for general target distributions in the near field and wide-band signals.

Correlation processing for correction of phase distortions in subaperture imaging

Ultrasonic subaperture imaging combines synthetic aperture and phased array approaches and permits low-cost systems with improved image quality. In subaperture processing, a large array is synthesized using echo signals collected from a number of receive subapertures by multiple firings of a phased transmit subaperture. Tissue inhomogeneities and displacements in subaperture imaging may cause significant phase distortions on received echo signals. Correlation processing on reference echo signals can be used for correction of the phase distortions, for which the accuracy and robustness are critically limited by the signal correlation. In this study, we explore correlation processing techniques for adaptive subaperture imaging with phase correction for motion and tissue inhomogeneities. The proposed techniques use new subaperture data acquisition schemes to produce reference signal sets with improved signal correlation. The experimental test results were obtained using raw radio frequency (RF) data acquired from two different phantoms with 3.5 MHz, 128-element transducer array. The results show that phase distortions can effectively be compensated by the proposed techniques in real-time adaptive subaperture imaging.

Phase aberration correction using near-field signal redundancy. II. Experimental results

For pt.I see ibid., vol.44, no.2, pp.355-71. A phase-aberration correction algorithm using near-field signal redundancy was proposed in part I. Here, this algorithm is tested on data collected from phantoms and volunteers. A linear array transducer was used with a synthetic-aperture scanning system. A wedge of plastic gel was used to introduce phase aberrations when collecting data from a phantom. About 40 sets of RF data were collected from eight volunteers. Results from both phantom and volunteer data have shown that the near-field signal redundancy algorithm can improve image quality by correcting phase aberrations when they are present. The results also show that this algorithm is robust.