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 /spl sim/62 ns, with interchannel correlation lengths as short as 1.4 mm.     

Experimental results with a real-time adaptive ultrasonic imaging system for viewing through distorting media

An online adaptive phased-array ultrasonic imaging system capable of markedly improving the detectability of targets viewed through inhomogeneous media is described. An online adaptive phase correction technique implemented on a research phased-array scanner is described. The theoretical basis for this technique is presented by describing the relationship between the magnitude of phase aberrations and the regional brightness of speckle and pointlike targets. The system currently generates a corrected image in approximately 0.1 s and utilizes no prior knowledge of the aberrating media or the target. The adaptive imaging algorithm uses regional target brightness as a quality factor. The results of in vitro tests with this system using electronic and physical aberrators for both diffuse and pointlike targets are presented.     

Demonstrated resolution enhancement capability of a stripmap holographic aperture ladar system

Holographic aperture ladar (HAL) is a variant of synthetic aperture ladar (SAL). The two processes are related in that they both seek to increase cross-range (i.e., the direction of the receiver translation) image resolution through the synthesis of a large effective aperture. This is in turn achieved via the translation of a receiver aperture and the subsequent coherent phasing and correlation of multiple received signals. However, while SAL imaging incorporates a translating point detector, HAL takes advantage of a two-dimensional translating sensor array. For the research presented in this article, a side-looking stripmap HAL geometry was used to sequentially image a set of Ronchi ruling targets. Prior to this, theoretical calculations were performed to determine the baseline, single subaperture resolution of our experimental, laboratory-based system. Theoretical calculations were also performed to determine the ideal modulation transfer function (MTF) and expected cross-range HAL image sharpening ratio corresponding to the geometry of our apparatus. To verify our expectations, we first sequentially captured an oversampled collection of pupil plane field segments for each Ronchi ruling. A HAL processing algorithm incorporating a high-precision speckle field registration process was then employed to phase-correct and reposition the field segments. Relative interframe piston phase errors were also removed prior to final synthetic image formation. By then taking the Fourier transform of the synthetic image intensity and examining the fundamental spatial frequency content, we were able to produce experimental modulation transfer function curves, which we then compared with our theoretical expectations. Our results show that we are able to achieve nearly diffraction-limited results for image sharpening ratios as high as 6.43.     

Aberrator integration error in adaptive imaging

Tissue speed of sound inhomogeneities cause significant degradation of medical ultrasound images. In some cases these inhomogeneities may be modeled as a thin time delay screen located at the face of the transducer. The effects of such near-field aberrations can be reduced by adding compensating time delays to the normal system focusing delays. Unfortunately array elements are generally large in at least one dimension when compared to variations in the aberrator, thus correction of the mean time delay on an element leaves residual variations in the time delay profile across that element. This paper presents theoretical expressions and simulation results describing the magnitude of this aberrator integration error. Simulations results are also presented which show the distortion of received pulses and degradation of point spread functions which results from aberrator integration error. These results indicate that aberrator integration error may be the dominant source of error in the implementation of adaptive imaging techniques and in phase aberration measurements. Thus, correction of near-field aberrations may be significantly more difficult than previously suspected     

Time-shift estimation and focusing through distributed aberrationusing multirow arrays

The effects of element height on time-shift estimation and transmit focus compensation are demonstrated experimentally. Multirow ultrasonic transducer arrays were emulated by combining adjacent elements of a 3.0-MHz, 0.6-mm pitch, two-dimensional array to define larger virtual elements. Pulse-echo data were acquired through tissue-mimicking distributed aberrators, and time-shift maps estimated from those data were used for transmit focus compensation. Compensated beams formed by arrays with fine row pitches were similar, but focus restoration was significantly less effective for "1.75-D" arrays with a coarse row pitch. For example, when focus compensation was derived from strongly aberrated random scattering data [70-ns nominal rms arrival time fluctuation with 7 mm FWHM (full-width at half-maximum) correlation length], the mean -20 dB lateral beamwidths were 5.2 mm for f/2.0 arrays with 0.6- and 1.8-mm row pitches and 9.5 mm for an f /2.0 array with 5.4-mm pitch. Time-shift maps estimated from random scattering data acquired with 5.4-mm pitch arrays included large discontinuities caused by low correlation of signals received on vertically and diagonally adjacent emulated elements. The results indicate that multirow arrays designed for use with aberration correction should have element dimensions much less than 75% of the correlation length of the aberration and perhaps as small as 25 to 30% of the correlation length     

Impact of propagation through an aberrating medium on the linear effective apodization of a nonlinearly generated second harmonic field

Techniques based on the nonlinearly generated second harmonic signal (tissue harmonic imaging) have rapidly supplanted linear (fundamental) imaging methods as the standard in two-dimensional echocardiography. Enhancements to the compactness of the nonlinearly generated second harmonic (2f) field component with respect to the fundamental (1f) field component are widely considered to be among the factors contributing to the observed image quality improvements. The objective of this study was to measure the impact of phase and amplitude aberrations resulting from propagation through an inhomogeneous tissue, on the beamwidths associated with: the fundamental (1f); the nonlinearly generated second harmonic (2f); and the linearly propagated, effective apodization signal at the same (21) frequency. Modifications to the transmit characteristics of a phased-array imaging system were validated with hydrophone measurements. Results demonstrate that the characteristics of the diffraction pattern associated with the linear-propagation effective apodization transmit case were found to be in good agreement with the detailed spatial characteristics of the nonlinearly generated second harmonic field. The effects of the abdominal wall tissue aberrators are apparent for all three of the beam profiles studied. Consistent with the improved image quality associated with harmonic imaging, the aberrated nonlinearly generated second harmonic beam was shown to remain more compact than the corresponding aberrated fundamental beam patterns in the presence of the interposed aberrator.     

Operational verification of a 40-MHz annular array transducer

An experimental system to take advantage of the imaging capabilities of a 5-ring polyvinylidene fluoride (PVDF)-based annular array is presented. The array has a 6-mm total aperture and a 12-mm geometric focus. The experimental system is designed to pulse a single element of the array and then digitize the received data of all array channels simultaneously. All transmit/receive pairs are digitized and then the data are post-processed with a synthetic-focusing technique to achieve an enhanced depth of field (DOF). The performance of the array is experimentally tested with a wire phantom consisting of 25-microm diameter wires diagonally spaced at 1-mm by 1-mm intervals. The phantom permitted the efficacy of the synthetic-focusing algorithm to be tested and was also used for two-way beam characterization. Experimental results are compared to a spatial impulse response method beam simulation. After synthetic focusing, the two-way echo amplitude was enhanced over the range of 8 to 19 mm and the 6-dB DOF spanned from 9 to 15 mm. For a wire at a fixed axial depth, the relative time delays between transmit/receive ring pairs agreed with theoretical predictions to within +/- 2 ns. To further test the system, B-mode images of an excised bovine eye were rendered.     

A split-aperture transmit beamforming technique with phase coherence grating lobe suppression

A small element-to-element pitch (~.5λ) is conventionally required for phased array ultrasound transducers to avoid large grating lobes. This constraint can introduce many fabrication difficulties, particularly in the development of highfrequency phased arrays at operating frequencies greater than 30 MHz. In this paper, a new transmit beamforming technique along with sign coherence factor (SCF) receive beamforming is proposed to suppress grating lobes in large-pitch phased-array transducers. It is based on splitting the transmit aperture (N elements) into N/K transmit elements and receive beamforming on all N elements to reduce the temporal length of the transmit grating lobe signal. Therefore, the use of synthetic aperture beamforming, which can introduce relative phase distortions between the echoes received over many transmit events, can be avoided. After each transmit-receive event, the received signals are weighted by the calculated SCF to suppress the grating lobes. After pulsing all sub-apertures, the RF signals are added to generate one line of the image. Simulated 2-way radiation patterns for different K values show that grating lobes can be suppressed significantly at different steering angles. Grating lobes can be suppressed by approximately 20 dB with K = 2 at steering angles greater than 25° and an element pitch greater than 0.75λ. A technique for determining the optimal transmit sub-apertures has been developed.     

Real-time 3-D ultrasound imaging using sparse synthetic aperture beamforming

A method for real-time three-dimensional (3-D) ultrasound imaging using a mechanically scanned linear phased array is proposed. The high frame rate necessary for real-time volumetric imaging is achieved using a sparse synthetic aperture beamforming technique utilizing only a few transmit pulses for each image. Grating lobes in the two-way radiation pattern are avoided by adjusting the transmit element spacing and the receive aperture functions to account for the missing transmit elements. The signal loss associated with fewer transmit pulses is minimized by increasing the power delivered to each transmit element and by using multiple transmit elements for each transmit pulse. By mechanically rocking the array, in a way similar to what is done with an annular array, a 3-D set of images can be collected in the time normally required for a single image.     

Efficient transmit beamforming in pulse-echo ultrasonic imaging

A high performance ultrasound imaging system requires accurate control of the amplitude of the array elements, as well as of the time delays between them, both in the transmit and receive modes. In transmission, conventional array aperture windowing implies a different driving voltage for each element of the array, an expensive solution for systems with a large number of channels. In this paper, we present a simple, versatile, and inexpensive beamforming method that operates the aperture windowing in the transmit mode, simply controlling the lengths of the electric pulses driving the array elements. Computer simulations and experimental measurements are presented for different types of arrays. They confirm that the proposed beamforming technique improves the contrast resolution of the imaging system, reducing the off-axis intensity of the radiated field pattern. Moreover, the axial resolution is slightly enhanced, because the overall length of the transmitted ultrasonic pulse is reduced.     

采用反向投影算法进行宽带合成孔径声纳数据处理与图像重建

文中提出了宽带合成孔径声纳(synthetic aperture Sonar，简称SAS)成像的反向投影算法(back pmjection，简称BP)。该算法是在时间-空间域中对合成孔径线列阵中备个阵元接收回波的所有频率分量进行相干求和，以充分利用合成孔径上所有回波的能量，从而得到理想的SAS图像。同时，文章中分析了BP算法实现过程中拖尾(tall)现象的产生机理，对BP重建图像进行了斜坡滤波处理。并对载频为15kHz,带宽为20kHz的SAS系统进行了仿真，结果验证了这种算法的有效性。     

Ultrasonic Imaging Algorithms With Limited Transmission Cycles for Rapid Nondestructive Evaluation

Imaging algorithms recently developed in ultrasonic nondestructive testing (NDT) have shown good potential for defect characterization. Many of them are based on the concept of collecting the full matrix of data, obtained by firing each element of an ultrasonic phased array independently, while collecting the data with all elements. Because of the finite sound velocity in the test structure, 2 consecutive firings must be separated by a minimum time interval. Depending on the number of elements in a given array, this may become problematic if data must be collected within a short time, as it is often the case, for example, in an industrial context. An obvious way to decrease the duration of data capture is to use a sparse transmit aperture, in which only a restricted number of elements are used to transmit ultrasonic waves. This paper compares 2 approaches aimed at producing an image on the basis of restricted data: the common source method and the effective aperture technique. The effective aperture technique is based on the far-field approximation, and no similar approach exists for the near-field. This paper investigates the performance of this technique in near-field conditions, where most NDT applications are made. First, these methods are described and their point spread functions are compared with that of the total focusing method (TFM), which consists of focusing the array at every point in the image. Then, a map of efficiency is given for the different algorithms in the nearfield. The map can be used to select the most appropriate algorithm. Finally, this map is validated by testing the different algorithms on experimental data.     

Vector Field Smoothing for DOA Estimation of Coherent Underwater Acoustic Signals in Presence of a Reflecting Boundary

A new vector field smoothing algorithm for direction-of-arrival (DOA) estimation of multiple coherent, underwater acoustic signals is proposed based on the array with vector hydrophones, which is located at or near a reflecting boundary. The performance of the proposed algorithm is examined in two practical applications: hull-mounted and seabed array. The advantage of the vector field smoothing scheme is no reduction in the overall array's spatial aperture.     

Analysis and numerical computation of diffraction of an optical field by a subwavelength-size aperture in a thick metallic screen by use of a volume integral equation

Diffraction of an optical field by an aperture in a thick metallic screen is analyzed numerically by use of a three-dimensional volume integral equation together with a generalized conjugate residual method and fast Fourier transformation. Numerical results were validated by reciprocity and the independence of the results of the truncated discretized volume size used in numerical calculations. Near and far fields of square, circular, and triangular apertures in a thick screen are obtained numerically. Some of the numerical results obtained in the present study agree with previously reported experimental results. The surface plasmon polaritons excited on the sidewalls of the aperture can explain the basic characteristics of near-field distribution of apertures. The Bethe-Bouwkamp theory was found to be insufficient to explain the basic characteristics of the near field around the subwavelength aperture in a practical metallic screen.     

基于重叠互相关器的合成孔径水池实验研究

在过去十几年里,为了增加拖曳线列阵系统的空间增益、提高方位分辨率,各种合成孔径技术应运而生。针对AUV舷侧阵系统水下目标远程探测的研究需要,给出了基于重叠互相关器的合成孔径处理算法(OCSAP),这种方法是在假设AUV旁侧阵匀速直线航行前提下,通过在波束域利用FFT变换合成孔径,并且在连续的时间间隔内对子孔径信号进行相关处理来实现的。在对该算法进行计算机仿真研究的基础上,在消声水池中进行了8阵元合成48阵元以及单阵元合成8阵元的逆合成孔径实验研究,两种实验结果均验证了OCSAP算法的有效性和可行性。实验结果表明合成孔径处理与常规物理孔径处理相比具有较好的鲁棒性,并且在接收信号时域相关长度大于合成孔径所需时间的水下或海洋环境里,合成阵增益与等长的物理阵增益基本相等。     

Synthetic aperture imaging for small scale systems

Multi-element synthetic aperture imaging methods suitable for applications with severe cost and size limitations are explored. Array apertures are synthesized using an active multi-element receive subaperture and a multi-element transmit subaperture defocused to emulate a single-element spatial response with high acoustic power. Echo signals are recorded independently by individual elements of the receive subaperture. Each method uses different spatial frequencies and acquisition strategies for imaging, and therefore different sets of active transmit/receive element combinations. Following acquisition, image points are reconstructed using the complete data set with full dynamic focus on both transmit and receive. Various factors affecting image quality have been evaluated and compared to conventional imagers through measurements with a 3.5 MHz, 128-element transducer array on different gel phantoms. Multielement synthetic aperture methods achieve higher electronic signal to noise ratio and better contrast resolution than conventional synthetic aperture techniques, approaching conventional phased array performance     

Adaptive compensation of phase and magnitude aberrations

A new method for aberration correction is presented. Using multiple receive beams reconstructed at each transmit direction, image artifacts due to imperfect beam forming can be identified and greatly reduced. Previous studies have demonstrated the efficacy of such a compensation algorithm for blocked elements. In this study, the algorithm is extended for magnitude and phase aberrations. Experimental results show that substantial improvements are possible for small amplitude and phase errors. The compensation method is less effective for large errors, however. Based on this, a two-step procedure is proposed for general aberration correction. First, cross-correlation processing is used to reduce significant phase errors. Then, the adaptive compensation method is applied to remove remaining artifacts due to blocked elements, amplitude aberrations, and residual phase errors. This two-step procedure is shown to be effective in significantly reducing image artifacts due to amplitude and phase errors     

On the importance of path for phase unwrapping in synthetic aperture radar interferometry

Phase unwrapping is a key procedure in interferometric synthetic aperture radar studies, translating ambiguous phase observations to topography, and surface deformation estimates. Some unwrapping algorithms are conducted along specific paths based on different selection criteria. In this study, we analyze six unwrapping paths: line scan, maximum coherence, phase derivative variance, phase derivative variance with branch-cut, second-derivative reliability, and the Fisher distance. The latter is a new path algorithm based on Fisher information theory, which combines the phase derivative with the expected variance to get a more robust path, potentially performing better than others in the case of low image quality. In order to compare only the performance of the paths, the same unwrapping function (phase derivative integral) is used. Results indicate that the Fisher distance algorithm gives better results in most cases.     

合成孔径声呐时延估计误差校正改进算法

由相位解缠错误造成的时延估计误差会严重降低合成孔径声呐时延估计的精度。现有的时延估计误差校正算法采用二次函数作为时延的拟合模型,该模型在距离向近端和远端处不符合时延空变规律,拟合误差较大且无法估计载体的横荡和升沉运动。针对该问题,文章提出一种改进的时延估计误差校正算法,利用时延的距离空变函数代替二次函数作为拟合模型。数值仿真和实验结果表明,相较于参考算法,改进算法校正时延估计误差的效果更好、速度更快,同时还能准确地估计载体的横荡和升沉运动。运动补偿结果显示了改进算法能较好地提升成像质量。     

聚焦矩阵在水中宽带目标被动跟踪中的应用

针对水中机动宽带目标,对于设计好的均匀线列阵,采用空间重采样方法计算基阵的恒定束宽阵元权系数,进而利用该阵元权系数产生聚焦矩阵,通过聚焦矩阵将不同频带的子带信号映射到同一参考频率上,然后将所有频率成分的信号功率谱密度矩阵作平均,并结合MUSIC(Multiple Signal Classification)算法,估计出目标的方位信息,从而实现水中宽带目标的被动跟踪。采用该方法进行仿真试验分析,结果表明在小孔径基阵上可实现宽带单目标的稳定测向被动跟踪,且对多目标具有一定的角被动分辨效果。