A novel power spectrum calculation method using phase-compensation and weighted averaging for the estimation of ultrasound attenuation

An estimation of ultrasound attenuation in soft tissues is critical in the quantitative ultrasound analysis since it is not only related to the estimations of other ultrasound parameters, such as speed of sound, integrated scatterers, or scatterer size, but also provides pathological information of the scanned tissue. However, estimation performances of ultrasound attenuation are intimately tied to the accurate extraction of spectral information from the backscattered radiofrequency (RF) signals. In this paper, we propose two novel techniques for calculating a block power spectrum from the backscattered ultrasound signals. These are based on the phase-compensation of each RF segment using the normalized cross-correlation to minimize estimation errors due to phase variations, and the weighted averaging technique to maximize the signal-to-noise ratio (SNR). The simulation results with uniform numerical phantoms demonstrate that the proposed method estimates local attenuation coefficients within 1.57% of the actual values while the conventional methods estimate those within 2.96%. The proposed method is especially effective when we deal with the signal reflected from the deeper depth where the SNR level is lower or when the gated window contains a small number of signal samples. Experimental results, performed at 5 MHz, were obtained with a one-dimensional 128 elements array, using the tissue-mimicking phantoms also show that the proposed method provides better estimation results (within 3.04% of the actual value) with smaller estimation variances compared to the conventional methods (within 5.93%) for all cases considered.     

目标图像结构和噪声对相关哈特曼-夏克波前传感精度的影响

以空间频谱描述图像结构,以图像灰度起伏的方均根值与噪声方均根值之比表示信噪比,系统分析了目标图像结构和噪声对相关哈特曼-夏克波前传感精度的影响。理论分析表明,两个子图像的相关函数峰值位置的亚像元插值误差等于其各离散频率成分的相关函数峰值位置插值误差的加权平均;相同功率下,低频成分的加权系数较小,高频成分的加权系数与亚像元偏移量有关。一维窄带图像的统计仿真表明,无噪声时,低频成分和接近奈奎斯特频率成分的误差较大,中频成分的误差较小;有噪声时,噪声对高频成分的影响低于低频成分。对典型频谱的32×32图像仿真表明,图像起伏信噪比为2∶1时,子图像平移量计算误差约0.03~0.11像元,与无噪声时相比增加不大。     

Improved scatterer property estimates from ultrasound backscatter for small gate lengths using a gate-edge correction factor

Backscattered rf signals used to construct conventional ultrasound B-mode images contain frequency-dependent information that can be examined through the backscattered power spectrum. The backscattered power spectrum is found by taking the magnitude squared of the Fourier transform of a gated time segment corresponding to a region in the scattering volume. When a time segment is gated, the edges of the gated regions change the frequency content of the backscattered power spectrum due to truncating of the waveform. Tapered windows, like the Hanning window, and longer gate lengths reduce the relative contribution of the gate-edge effects. A new gate-edge correction factor was developed that partially accounted for the edge effects. The gate-edge correction factor gave more accurate estimates of scatterer properties at small gate lengths compared to conventional windowing functions. The gate-edge correction factor gave estimates of scatterer properties within 5% of actual values at very small gate lengths (less than 5 spatial pulse lengths) in both simulations and from measurements on glass-bead phantoms. While the gate-edge correction factor gave higher accuracy of estimates at smaller gate lengths, the precision of estimates was not improved at small gate lengths over conventional windowing functions.     

Identifying ultrasonic scattering sites from three-dimensional impedance maps

Ultrasonic backscattered signals contain frequency-dependent information that is usually discarded to produce conventional B-mode images. It is hypothesized that parametrization of the quantitative ultrasound frequency-dependent information (i.e., estimating scatterer size and acoustic concentration) may be related to discrete scattering anatomic structures in tissues. Thus, an estimation technique is proposed to extract scatterer size and acoustic concentration from the power spectrum derived from a three-dimensional impedance map (3DZM) of a tissue volume. The 3DZM can be viewed as a computational phantom and is produced from a 3D histologic data set. The 3D histologic data set is constructed from tissue sections that have been appropriately stained to highlight specific tissue features. These tissue features are assigned acoustic impedance values to yield a 3DZM. From the power spectrum, scatterer size and acoustic concentration estimates were obtained by optimization. The 3DZM technique was validated by simulations that showed relative errors of less than 3% for all estimated parameters. Estimates using the 3DZM technique were obtained and compared against published ultrasonically derived estimates for two mammary tumors, a rat fibroadenoma and a 4T1 mouse mammary carcinoma. For both tumors, the relative difference between ultrasonic and 3DZM estimates was less than 10% for the average scatterer size.     

Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.     

Defining optimal axial and lateral resolution for estimating scatterer properties from volumes using ultrasound backscatter

The rf signals used to construct conventional ultrasound B-mode images contain frequency-dependent information that can be examined through the backscattered power spectrum. Typically, the backscattered power spectrum is calculated from a region of interest (ROI) within some larger volume. The dimensions of the ROI are defined axially by the spatial length corresponding to the time gate and laterally by the number of scan lines included in the ROI. Averaging the backscattered power spectra from several independent scan lines can reduce the presence of noise caused by electronics and by the random scatterer spacings, but also decreases the lateral resolution of the interrogation region. Furthermore, larger axial gate lengths can be used to reduce the effects of noise and improve the precision and accuracy of scatterer property estimates but also decreases the axial resolution. A trade-off exists between the size of the ROI (the number of scan lines used, the separation distance between each scan line, the axial gate length) and the accuracy and precision of scatterer property estimates. A series of simulations and measurements from physical phantoms were employed to examine these trade-offs. The simulations and phantom measurements indicated the optimal lateral and axial sizes of the ROI, where estimate accuracy and precision were better than 10% and 5%, respectively, occurred at 4 to 5 beamwidths laterally and 15 to 20 spatial pulse lengths axially.     

Experimental study of the Doppler shift generated by a vibrating scatterer

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F < f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 > F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA < 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.     

The detection of temporal gaps as a function of frequency region and absolute noise bandwidth.

Temporal gap detection was measured as a function of absolute signal bandwidth at a low-, a mid-, and a high-frequency region in six listeners with normal hearing sensitivity. Gap detection threshold decreased monotonically with increasing stimulus bandwidth at each of the three frequency regions. Given conditions of equivalent absolute bandwidth, gap detection thresholds were not significantly different for upper cutoff frequencies ranging from 600 to 4400 Hz. A second experiment investigated gap detection thresholds at two pressure-spectrum levels, conditions typically resulting in substantially different estimates of frequency selectivity. Estimates of frequency selectivity were collected at the two levels using a notched-noise masker technique. The gap threshold-signal bandwidth functions were almost identical at pressure-spectrum levels of 70 dB and 40 dB for the two subjects in experiment II, while estimates of frequency selectivity showed poorer frequency selectivity at the 70-dB level than at 40 dB. Data from both experiments indicated that gap detection in bandlimited noise was inversely related to signal bandwidth and that gap detection did not vary significantly with changes in signal frequency over the range of 600 to 4400 Hz. Over the range of frequencies investigated, the results indicated no clear relation between gap detection for noise stimuli and peripheral auditory filtering.     

Attenuation measurement uncertainties caused by speckle statistics

Attenuation measurements can be derived from the decay of backscattered signal with depth in an inhomogeneous material. In cases such as liver tissue, where many small inhomogeneities are likely to be included in sample volumes defined by pulse and beam widths, Rayleigh statistics describe the random nature of the magnitude of backscattered pressure. The statistics of speckle underlie the uncertainties in estimates of attenuation at discrete frequencies, and of the magnitude and frequency dependence of attenuation over a bandwidth. This paper derives expressions for the standard deviations of attenuation magnitude and frequency dependence in terms of parameters such as the dimensions of the region of interest, and the bandwidth of the ultrasonic system. Practical examples are given using published data, and comparisons to other techniques which measure "attenuation slope" are made. The analysis yields insights into trade-offs among variables such as the dimensions and shape of regions of interest, and the segmenting of data in time and frequency domain.     

具有频率噪声的单模激光线性模型随机共振

将频率有涨落的周期信号输入单模激光增益模型,计算出输出光强的相关函数及功率谱,对信噪比随噪声强度和系统参数的变化进行了研究. 结果表明:信噪比随频率噪声强度的变化、抽运噪声强度的变化、量子噪声强度的变化均出现随机共振;信噪比随增益系数和损失系数的变化也出现随机共振. 关键词： 频率噪声 功率谱 随机共振     

调幅波的单模激光线性模型随机共振

对单模激光增益模型的光强方程加入调幅波，用线性化近似方法计算了以δ函数形式关联的两白噪声驱动下光强的输出功率谱及信噪比. 结果表明，信噪比不但随着抽运噪声和量子噪声强度的变化出现随机共振，而且随着高频载波信号频率和低频调制信号频率的变化也出现了随机共振. 关键词： 抽运噪声 单模激光 随机共振 调幅波     

偏置调幅波调制噪声的单模激光随机共振

采用偏置信号的调幅波调制抽运噪声的单模激光增益模型，用线性化近似方法计算了以e指数形式关联的两色噪声驱动下光强的功率谱及信噪比.结果表明，信噪比随着噪声强度的变化、抽运噪声自关联时间的变化、激光系统参数的变化、载波频率及信号频率的变化均存在随机共振现象. 关键词： 抽运噪声 单模激光 随机共振 调幅波     

解调带宽对船舶辐射噪声调制谱的影响

利用傅里叶分解原理建立了幅度调制的船舶辐射宽带噪声信号数学模型,导出了基于平方解调算法船舶辐射噪声调制谱数学表达式。通过理论分析和仿真计算得到了关于调制谱分析两个新的结论:(1)解调性能与解调处理带宽关系:在声呐接收的船舶辐射噪声各频带调制度相同时,解调性能正比于解调所采用的带通滤波带宽,解调所采用的带通滤波带宽越宽,解调谱信噪比越高;(2)宽带解调谱和子频带解调谱之间关系:船舶辐射噪声宽带解调谱可以近似认为各子频带解调谱之和。为了验证以上两点结论,对实际船舶辐射噪声解调谱进行了相应处理,结果与仿真计算吻合较好。      

调频信号的单模激光线性模型随机共振

对单模激光增益模型的光强方程加入调频信号,用线性化近似方法计算了以δ函数形式关联的两白噪声驱动下光强的输出功率谱及信噪比. 结果表明,信噪比随抽运噪声和量子噪声强度的变化可出现典型随机共振,受调制信号振幅的影响,信噪比随载波信号频率和调制信号频率的变化出现抑制、单调上升、共振、抑制和共振等几种情况. 关键词： 抽运噪声 单模激光 随机共振 调频信号     

Different auditory filter bandwidth estimates based on profile analysis, notched noise, and hybrid tasks

Auditory filter bandwidths were estimated in three experiments. The first experiment was a profile-analysis experiment. The stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 Hz. The standard stimulus was the sum of equal-amplitude tones, and the signal stimulus had a power spectrum that varied up-down ... up-down. The number of components ranged from four to 60. Interval-by-interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal. The second experiment was a notched-noise experiment in which the 1000-Hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 Hz. Detection thresholds were estimated both in the presence of and in the absence of level randomization. In the third, hybrid, experiment a 1000-Hz tone was to be detected, and the masker was composed of equal-amplitude sinusoidal components ranging in frequency from 200 to 5000 Hz. For this experiment, thresholds were estimated both in the presence and absence of level variation. For both the notched-noise and hybrid experiments, only modest effects of level randomization were obtained. A variant of Durlach et al.'s channel model ["Towards a model for discrimination of broadband signals," J. Acoust. Soc. Am. 80, 63-72 (1986)] was used to estimate auditory filter bandwidths for all three experiments. When a two-parameter roex(p,r) filter weighting function was used to fit the data, bandwidth estimates were approximately two to three times as large for the two detection tasks than for the profile-analysis task.     

Describing small-scale structure in random media using pulse-echo ultrasound

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.     

Statistics of ultrasonic scatterer size estimation with a reference phantom

A theoretical expression for the variance of scatterer size estimates is derived for a modified least squares size estimator used in conjunction with a reference phantom method for backscatter coefficient measurement. A Gaussian spatial autocorrelation function is assumed. Simulations and phantom experiments were performed to verify the results for backscatter and size variances. The dependence of size estimate errors upon free experimental parameters is explored. Implications of the findings for the optimization of scatterer size estimation are discussed. The utility of scatterer size parametric imaging is examined through the signal to noise ratio comparison with standard ultrasonic B-mode imaging.     

一阶线性系统的调参随机共振研究

分析了一阶线性系统在正弦和白噪声信号作用下的输出功率谱和信噪比.研究表明,加性噪声作用下的线性系统不存在传统意义上的随机共振,但却存在输出信噪比随系统参数非单调变化的调参广义随机共振现象.针对任意频率信号,分析了不同采样频率下的调参共振谱特性,得出适当增大采样频率有利于特征信号识别的结论.     

Behavioral measures of frequency selectivity in the chinchilla.

A simultaneous masking procedure was used to derive four measures of frequency selectivity in the chinchilla. The first experiment measured critical masking ratios (CRs) at various signal frequencies. Estimates of the chinchillas' critical bandwidths derived from the CRs were much broader than comparable human estimates, indicating that the chinchilla may have inferior frequency selectivity. The second experiment measured critical bandwidths at 1, 2, and 4 kHz in a band-narrowing experiment. This technique yielded narrower estimates of critical bandwidth; however, chinchillas continued to exhibit poor frequency selectivity compared to man. The third experiment measured auditory-filter shape at 0.5, 1, and 2 kHz via rippled noise masking. Results of the rippled noise masking experiment indicate that auditory filters of humans and chinchillas are similar in terms of shape and bandwidth with chinchillas showing only slightly poorer frequency selectivity. The final experiment measured auditory filter shape at 0.5, 1, 2, and 4 kHz using notched noise masking. This experiment yielded auditory filter shapes and bandwidths similar to those derived from man. The discrepancy between the indirect estimates of frequency selectivity derived from CR and band-narrowing techniques and the direct estimates derived from rippled noise and notched noise masking are explained by taking into account the processing efficiency of the subjects.     

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain--noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.