Iteration of transmit-beam aberration correction in medical ultrasound imaging

Simulations of iterative transmit-beam aberration correction using a time-delay and amplitude filter have been performed to study the convergence of such a process. Aberration in medical ultrasonic imaging is usually modeled by arrival-time and amplitude fluctuations concentrated on the transducer array. This is an approximation of the physical aberration process, and may be applied to correct the transmitted signal using a time-delay and amplitude filter. Estimation of such a filter has proven difficult in the presence of severe aberration. Presented here is an iterative approach, whereby a filter estimate is applied to correct the transmit-beam. This beam induces acoustic backscatter better suited for arrival-time and amplitude estimation, thus facilitating an improved filter estimate. Two correlation-based methods for estimating arrival-time and amplitude fluctuations in received echoes from random scatterers were employed. Aberration was introduced using eight models emulating aberration produced by the human abdominal wall. Results show that only a few iterations are needed to obtain corrected transmit-beam profiles comparable to those of an ideal aberration correction filter. Furthermore, a previously developed focusing criterion is found to quantify the convergence accurately.     

Spectral estimation for characterization of acoustic aberration

Spectral estimation based on acoustic backscatter from a motionless stochastic medium is described for characterization of aberration in ultrasonic imaging. The underlying assumptions for the estimation are: The correlation length of the medium is short compared to the length of the transmitted acoustic pulse, an isoplanatic region of sufficient size exists around the focal point, and the backscatter can be modeled as an ergodic stochastic process. The motivation for this work is ultrasonic imaging with aberration correction. Measurements were performed using a two-dimensional array system with 80 x 80 transducer elements and an element pitch of 0.6 mm. The f number for the measurements was 1.2 and the center frequency was 3.0 MHz with a 53% bandwidth. Relative phase of aberration was extracted from estimated cross spectra using a robust least-mean-square-error method based on an orthogonal expansion of the phase differences of neighboring wave forms as a function of frequency. Estimates of cross-spectrum phase from measurements of random scattering through a tissue-mimicking aberrator have confidence bands approximately +/- 5 degrees wide. Both phase and magnitude are in good agreement with a reference characterization obtained from a point scatterer.     

Harmonic source wavefront aberration correction for ultrasound imaging

A method is proposed which uses a lower-frequency transmit to create a known harmonic acoustical source in tissue suitable for wavefront correction without a priori assumptions of the target or requiring a transponder. The measurement and imaging steps of this method were implemented on the Duke phased array system with a two-dimensional (2-D) array. The method was tested with multiple electronic aberrators [0.39π to 1.16π radians root-mean-square (rms) at 4.17 MHz] and with a physical aberrator 0.17π radians rms at 4.17 MHz) in a variety of imaging situations. Corrections were quantified in terms of peak beam amplitude compared to the unaberrated case, with restoration between 0.6 and 36.6 dB of peak amplitude with a single correction. Standard phantom images before and after correction were obtained and showed both visible improvement and 14 dB contrast improvement after correction. This method, when combined with previous phase correction methods, may be an important step that leads to improved clinical images.     

Distributed delays facilitate amplitude death of coupled oscillators

Coupled oscillators are shown to experience amplitude death for a much larger set of parameter values when they are connected with time delays distributed over an interval rather than concentrated at a point. Distributed delays enlarge and merge death islands in the parameter space. Furthermore, when the variance of the distribution is larger than a threshold, the death region becomes unbounded and amplitude death can occur for any average value of delay. These phenomena are observed even with a small spread of delays, for different distribution functions, and an arbitrary number of oscillators.     

利用回波相干性的医学超声成像相位畸变校正方法

为了提高相位畸变条件下的医学超声成像的横向分辨率和对比度,提出了一种利用回波信号相干性的校正方法。首先给出平均相干系数的概念,并将其作为相位误差校正的度量,然后通过最大化平均相干系数逐步校正各个通道的延时误差,最后再利用经过校正的数据计算出一组新的相干系数并对回波信号进行加权优化,从而得到最终用于成像的数据。对点散射目标及斑散射目标的仿真结果分别显示,利用所提出的方法横向分辨率提高了约0.24 mm,对比度提高了约18 dB,且要优于邻近阵元互相关方法和相干系数直接加权的处理方法。利用回波相干性的相位畸变校正方法结合了相位误差校正和加权处理的优点,可以有效地改善医学超声成像的质量。      

Eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging

Presented here is a characterization of aberration in medical ultrasound imaging. The characterization is optimal in the sense of maximizing the expected energy in a modified beamformer output of the received acoustic backscatter. Aberration correction based on this characterization takes the form of an aberration correction filter. The situation considered is frequently found in applications when imaging organs through a body wall: aberration is introduced in a layer close to the transducer, and acoustic backscatter from a scattering region behind the body wall is measured at the transducer surface. The scattering region consists of scatterers randomly distributed with very short correlation length compared to the acoustic wavelength of the transmit pulse. The scatterer distribution is therefore assumed to be delta correlated. This paper shows how maximizing the expected energy in a modified beamformer output signal naturally leads to eigenfunctions of a Fredholm integral operator, where the associated kernel function is a spatial correlation function of the received stochastic signal. Aberration characterization and aberration correction are presented for simulated data constructed to mimic aberration introduced by the abdominal wall. The results compare well with what is obtainable using data from a simulated point source.     

A coherence-based phase aberration correction method in medical ultrasound

A coherence-based correction method was proposed in order to improve the lateral resolution and enhance the contrast of medical ultrasound imaging in the presence of phase aberration.The averaged coherence factor was proposed at first and used as a metric to evaluate phase aberration correction.By maximizing the averaged coherence factor,the time delay parameter of each channel was adjusted.A new set of coherence factors was calculated and the corrected data was optimized to form the final B-mode image.The simulations on point targets and a cyst phantom showed that the proposed method outperformed the nearest neighboring cross correlation method and conventional coherence-weighting method,and the lateral resolution and contrast ratio was improved by approximately 0.24mm and 18dB respectively.The proposed method combined the advantages of phase error correction and coherence-weighting,which could improve imaging qualities effectively in medical ultrasound.     

Measurements of ultrasonic pulse arrival time differences produced by abdominal wall specimens.

The influence of propagation medium inhomogeneities on pulsatile ultrasonic fields has been investigated experimentally. The study employed a special curved transducer to produce a hemispherical wave pulse and a linear array to measure the resulting field along a line in a plane. Translation of the array in the elevation direction yielded data over a two-dimensional aperture. Time delay across the aperture was calculated by adding delay differences obtained by cross-correlating signals on adjacent elements and noting the position of the cross-correlation peaks. Received waveforms were shifted an amount given by the difference between the actual arrival time and a calculated geometric delay to isolate arrival time differences due to propagation path inhomogeneities. Waveform and time delay difference plots as well as histograms and statistics derived from them for propagation through a water path and for propagation through five specimens of human abdominal wall indicate that arrival time fluctuations in the presence of human abdominal wall specimens are significantly greater than for a water path and that degradation in focusing through human abdominal wall can be expected in ultrasonic imaging systems that operate in the low megahertz range and employ a relatively large aperture.     

Techniques for phase correction in coherent ultrasound imaging systems

The problem of phase aberrations modeled as a near field thin phase screen is considered. Here three new techniques for phase aberration correction are presented. In the "central element" correction technique the echo-signal at each array element is aligned with the signal at the central array element. In the "variable speckle look-back" correction technique the signal at each array element is aligned with the sum of signals from all previously corrected elements. In the "variable central speckle look-back" correction technique the signal at each array element is aligned with the sum of signals from the central group of all previously corrected elements. The performance of new techniques for phase aberration correction is tested by means of simulating the point-spread function for both point and speckle targets. The results of simulation show that the new techniques have the better accuracy of phase correction than the classical "neighbor element" technique.     

A particle filtering approach for spatial arrival time tracking in ocean acoustics

The focus of this work is on arrival time and amplitude estimation from acoustic signals recorded at spatially separated hydrophones in the ocean. A particle filtering approach is developed that treats arrival times as "targets" and tracks their "location" across receivers, also modeling arrival time gradient. The method is evaluated via Monte Carlo simulations and is compared to a maximum likelihood estimator, which does not relate arrivals at neighboring receivers. The comparison demonstrates a significant advantage in using the particle filter. It is also shown that posterior probability density functions of times and amplitudes become readily available with particle filtering.     

Errors in ultrasonic scatterer size estimates due to phase and amplitude aberration

Current ultrasonic scatterer size estimation methods assume that acoustic propagation is free of distortion due to large-scale variations in medium attenuation and sound speed. However, it has been demonstrated that under certain conditions in medical applications, medium inhomogeneities can cause significant field aberrations that lead to B-mode image artifacts. These same aberrations may be responsible for errors in size estimates and parametric images of scatterer size. This work derives theoretical expressions for the error in backscatter coefficient and size estimates as a function of statistical parameters that quantify phase and amplitude aberration, assuming a Gaussian spatial autocorrelation function. Results exhibit agreement with simulations for the limited region of parameter space considered. For large values of aberration decorrelation lengths relative to aberration standard deviations, phase aberration errors appear to be minimal, while amplitude aberration errors remain significant. Implications of the results for accurate backscatter and size estimation are discussed. In particular, backscatter filters are suggested as a method for error correction. Limitations of the theory are also addressed. The approach, approximations, and assumptions used in the derivation are most appropriate when the aberrating structures are relatively large, and the region containing the inhomogeneities is offset from the insonifying transducer.     

输气管道泄漏的波达时差交叉定位方法*

为了实现对管道泄漏位置的三维定位,该文提出一种基于波达时差法的交叉定位方法。将传感器阵列布放在不同位置,通过波达时差法获取远场泄漏声源的两组空间方位信息,对两组方位交叉求取空间伪交点从而完成定位。建立泄漏定位实验平台,分析了多种互相关方法以及阵列孔径、布放间距、泄漏位置等因素对延时估计和定位精度的影响。实验结果表明:选取基本互相关法对泄漏信号的10 500 Hz分量进行互相关分析,能够获取稳定的延时估计结果;在有效信号检测范围内,增大阵列孔径和布放间距能有效减少误差;该文方法相较于现有波达时差法能有效提高距离原点4 m以上泄漏位置的定位精度。     

Time reversed reverberation focusing in a waveguide

Time reversal mirrors have been applied to focus energy at probe source locations and point scatterers in inhomogeneous media. In this paper, we investigate the application of a time reversal mirror to rough interface reverberation processing in a waveguide. The method is based on the decomposition of the time reversal operator which is computed from the transfer matrix measured on a source-receiver array [Prada et al., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. In a similar manner, reverberation data collected on a source-receiver array can be filtered through an appropriate temporal window to form a time reversal operator. The most energetic eigenvector of the time reversal operator focuses along the interface at the range corresponding to the filter delay. It is also shown that improved signal-to-noise ratio measurement of the time reversal operator can be obtained by ensonifying the water column with a set of orthogonal array beams. Since these methods do not depend upon a priori environmental information, they are applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide demonstrate this method.     

部分阵元参考法校正超声成像相位畸变的仿真研究

本文应用互相关技术在阵元接收射频信号噪比不同情况下，对部分阵元参考法校正超声成像位畸变进行了仿真实验。     

Conditions for identical position of optimal image plane for axial imaging with different values of f-number

By analysis of the dependence of longitudinal spherical aberration on the numerical aperture, it is possible to find such values of the numerical aperture, where spherical aberration is zero. Such values of the numerical aperture are called correction zones. The work theoretically analyses the described problem and equations are given for wave aberration coefficients using correction zones for spherical aberration of the third and the fifth order. Our work presents an analysis of optimal values of correction zones and an optimal position of the center of the reference sphere based on the variance of wave aberration for the image quality evaluation. Relations are described for calculation of correction zones of an optical system having an identical position of the optimal image plane for two values of the f-number. The analysis of optical systems using correction zones is performed on an example.     

Direct estimation of aberrating delays in pulse-echo imaging systems

Nearfield fluctuations in wave propagation velocity and system timing errors are among the sources of focusing aberrations in pulse-echo imaging systems. For situations in which the source of these errors can be modeled by a stationary phase aberrator placed in front of the transmitter and receiver aperture, appropriate electronic delays might be applied to the signals associated with each array element in order to restore the system to focus. A method is described and evaluated for estimating the set of aberrating delays in a linear array utilizing data from a single two-dimensional scan. The underlying principle is analogous to that of phase closure used for one-way passive interferometry and readily generalizes to two-dimensional arrays. Although the following theory is developed in the context of acoustic imaging, the general approach is applicable to other pulse-echo systems, such as radar.     

Robust tracking of moving sound source using multiple model Kalman filter

In this paper a novel method for tracking an active speaker in a noisy and reverberant environment by means of a spatially distributed microphone array is presented. Firstly, a sound source localization algorithm based on time delays of arrival (TDOA) in microphone pairs provides observed position estimates. Then these remarkably noisy estimates are filtered by a multiple model Kalman filter (MMKF) in order to obtain a smoothed trajectory of the speaker’s movement. Compared with the traditional Kalman filter (KF), simulated results prove the MMKF is more robust and effective in noisy environments.     

Aberration correction and its automatic control in scanning electron microscopes

An automatic aberration correction method has been implemented in scanning electron microscopes (SEM). Necessity of the automatic aberration correction is discussed. The procedure of the automatic aberration correction is explained in detail, where deconvolution techniques are used in order to extract probe information from SEM images. Due to the precise digitization and the usage of proper combinations of correction fields, linearity has been found between the amplitude of each aberration and the corresponding field strength. Experimental results are shown which demonstrate that the aberrations are corrected automatically by a linear feedback control method. After the automatic aberration correction, the image quality has been improved drastically.     

Characteristics of sound signals on a quasi-stationary track between the Josephine and Ampere Seamounts

Experimental data are presented on the measurement of the cross-correlation coefficients and the differences in the arrival times (temporal spectra) of acoustic signals transmitted through a 210-km-long quasi-stationary track in the Atlantic Ocean. At the summit of the Josephine Seamount, a continuous pseudonoise signal was emitted in the one-third-octave band with a mean frequency of 630 Hz. The signal was received at the Ampere Seamount by a 40-m flexible vertical array with a directivity pattern in the form of a static fan of 32 lobes. The width of each lobe was ～3°. At a signal-to-noise ratio of about 3 dB and with an incomplete resolution of multipath signals by the array, the correlation coefficients reached a value of 0.48. The rms fluctuations of the differences in the arrival times varied from 1.8 to 3.1 ms depending on the signal arrival angles. The factors responsible for the low correlation coefficients and the relatively high fluctuations of the arrival time differences are discussed. Apparently, one of the factors is the presence of short-period internal waves.     

双压电片变形镜像差校正能力

利用实测影响函数,通过数值仿真分析了有效孔径、光束入射角度对于20单元双压电片变形镜像差校正能力的影响。仿真结果表明:有效孔径为16 mm时,变形镜对于各阶像差的校正能力较好;而随着光束入射到变形镜角度的增大,变形镜对于像差的校正精度与校正幅度都会出现下降,但是如果能够将入射角控制在25以内,入射角度对变形镜的像差校正能力影响不大。