A successive parameter estimation algorithm for chirplet signal decomposition

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, and object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation.     

EMAT noise suppression using information fusion in stationary wavelet packets

An important issue in ultrasonic nondestructive testing is the detection of flaw echoes in the presence of background noise created by instrumentation and by clutter noise. Signal averaging, autoregressive analysis, spectrum analysis, matched filtering, and the wavelet transform have all been used to filter noise in ultrasonic signals. Widely-used wavelet threshold estimation algorithms are not designed for electromagnetic acoustic transducer (EMAT) pulse-echo signals, and therefore do not exploit their unique impulse nature. The approach to ultrasonic signal filtering proposed in this paper is based on stationary wavelet packet denoising with a threshold influenced by several information sources: a statistical echo detection, the amplitude distribution of the wavelet transform coefficients, and a priori known system frequency characteristics. The proposed method was evaluated on signals measured with EMAT probes and under various SNR conditions; it outperforms the wavelet transform with the Stein unbiased risk estimate (SURE) threshold estimation method and split-spectrum processing (SSP). The results indicate SNR enhancement of 19 dB with real EMAT data.     

Model-based estimation of ultrasonic echoes. Part I: analysis and algorithms

The patterns of ultrasonic backscattered echoes represent valuable information pertaining to the geometric shape, size, and orientation of the reflectors as well as the microstructure of the propagation path. Accurate estimation of the ultrasonic echo pattern is essential in determining the object/propagation path properties. In this study, we model ultrasonic backscattered echoes in terms of superimposed Gaussian echoes corrupted by noise. Each Gaussian echo in the model is a nonlinear function of a set of parameters: echo bandwidth, arrival time, center frequency, amplitude, and phase. These parameters are sensitive to the echo shape and can be linked to the physical properties of reflectors and frequency characteristics of the propagation path. We address the estimation of these parameters using the maximum likelihood estimation (MLE) principle, assuming that all of the parameters describing the shape of the echo are unknown but deterministic. In cases for which noise is characterized as white Gaussian, the MLE problem simplifies to a least squares (LS) estimation problem. The iterative LS optimization algorithms when applied to superimposed echoes suffer from the problem of convergence and exponential growth in computation as the number of echoes increases. In this investigation, we have developed expectation maximization (EM)-based algorithms to estimate ultrasonic signals in terms of Gaussian echoes. The EM algorithms translate the complicated superimposed echoes estimation into isolated echo estimations, providing computational versatility. The algorithm outperforms the LS methods in terms of independence to the initial guess and convergence to the optimal solution, and it resolves closely spaced overlapping echoes     

钢包耳轴根部焊缝的相控阵超声检测与信号处理

采用匹配追踪算法和小波变换对低信噪比(2dB和-5dB)钢包耳轴根部焊缝缺陷检测信号进行预处理对比分析,在定制试块上采用64阵元超声相控阵探头对深度为230mm的耳轴根部焊缝进行检测,并且结合基于Gabor原子库的匹配追踪算法对回波信号进行消噪后成像.结果表明,在低信噪比(-5dB)条件下,匹配追踪算法较小波变换有更好的预处理效果;对深度位于220mm和230mm处的钢包耳轴焊缝缺陷的实际检测信号进行去噪处理时,匹配追踪算法能够准确定位缺陷位置并显著提高缺陷处信噪比.     

Signal detection and noise suppression using a wavelet transform signal processor: application to ultrasonic flaw detection

The utilization of signal processing techniques in nondestructive testing, especially in ultrasonics, is widespread. Signal averaging, matched filtering, frequency spectrum analysis, neural nets, and autoregressive analysis have all been used to analyze ultrasonic signals. The Wavelet Transform (WT) is the most recent technique for processing signals with time-varying spectra. Interest in wavelets and their potential applications has resulted in an explosion of papers; some have called the wavelets the most significant mathematical event of the past decade. In this work, the Wavelet Transform is utilized to improve ultrasonic flaw detection in noisy signals as an alternative to the Split-Spectrum Processing (SSP) technique. In SSP, the frequency spectrum of the signal is split using overlapping Gaussian passband filters with different central frequencies and fixed absolute bandwidth. A similar approach is utilized in the WT, but in this case the relative bandwidth is constant, resulting in a filter bank with a self-adjusting window structure that can display the temporal variation of the signal's spectral components with varying resolutions. This property of the WT is extremely useful for detecting flaw echoes embedded in background noise. The detection of ultrasonic pulses using the wavelet transform is described and numerical results show good detection even for signal-to-noise ratios (SNR) of -15 dB. The improvement in detection was experimentally verified using steel samples with simulated flaws.     

Practical spread spectrum pulse compression for ultrasonic tissue imaging

Spread spectrum pulse compression is a signal processing algorithm that enhances critical system performance parameters such as signal-to-noise ratio, peak power requirements, minimum detectable signal, and total dynamic range. For this research, a digital, real-time, Barker coded, bi-phase modulator was designed and constructed, as well as a simple ultrasonic test tank containing both synthetic targets and excised goat's liver. Upon reception and demodulation of the spread spectrum ultrasonic echo, cross-correlation with a sidelobe suppression filter was performed. Due to limitations such as narrow bandwidth, and very short minimum ranges, a practical ultrasonic pulse compression system must be restricted to short code lengths. For 13 bit Barker code compression, the expected increase in signal-to-noise ratio of 11 dB was realized; at the same time greater than 30 dB of instantaneous dynamic range was maintained.     

Model-based estimation of ultrasonic echoes. Part II: Nondestructive evaluation applications

For Part I see ibid., vol.48, no.3, pp.787-802 (2001). Accurate estimation of the ultrasonic echo pattern leading to the physical property of the object is desirable for ultrasonic NDE (nondestructive evaluation) applications. In Part I of this study, we have presented a generalized parametric ultrasonic echo model, composed of a number of Gaussian echoes corrupted by noise, and algorithms for accurately estimating the parameters. In Part II of this study, we explore the merits of this model-based estimation method in ultrasonic applications. This method produces high resolution and accurate estimates for ultrasonic echo parameters, i.e., time of flight (TOF) amplitude, center frequency, bandwidth, and phase. Furthermore, it offers a solution to the deconvolution problem for restoration of the target response, i.e., ultrasonic reflection and transmission properties of materials, from the backscattered echoes. The model-based estimation method makes deconvolution possible in the presence of significant noise. It can also restore closely spaced overlapping echoes beyond the resolution of the measuring system. These properties of the estimation method are investigated in various ultrasonic applications such as transducer pulse-echo wavelet estimation, subsample time delay estimation, and thickness sizing of thin layers     

基于字典学习的主动声呐目标分类方法

主动声呐目标分类在军事和民用方面都有重要的应用和价值。文章基于稀疏表示理论,结合K-奇异值分解和正交匹配追踪算法,提出一种基于学习字典的稀疏表示分类方法（Dictionary Learning Sparse Representation Classification,DLSRC）。首先,利用K-奇异值分解算法训练各个类别目标回波信号,得到带有目标特征信息的类别字典,类别字典对信号具有良好表征能力并且带有目标类别信息;然后,利用正交匹配追踪算法和各个类别字典稀疏分解测试信号,得到各个类别字典下的稀疏系数后重构信号;最后,根据各个重构信号与测试信号的匹配度判定类别,得到分类准确率。结果显示,200个测试数据在信噪比分别为-5、-3、6 dB时,DLSRC法的分类准确率分别达到87%、89%、95.5%。不同信噪比下基于学习字典稀疏表示分类方法的准确率均高于已有的支持向量机（Support Vector Machine,SVM）、K-最近邻（K-Nearest Neighbor,KNN）和柔性最大值分类器（SoftMax）等分类方法,具有较好的分类性能。     

Ultrasonic scanner for in vivo measurement of cancellous bone properties from backscattered data

A dedicated ultrasonic scanner for acquiring RF echoes backscattered from the trabecular bone was developed. The design of device is based on the goal of minimizing of custom electronics and computations executed solely on the main computer processor and the graphics card. The electronic encoder-digitizer module executing all of the transmission and reception functions is based on a single low-cost field programmable gate array (FPGA). The scanner is equipped with a mechanical sector-scan probe with a concave transducer with 50 mm focal length, center frequency of 1.5 MHz and 60% bandwidth at -6 dB. The example of femoral neck bone examination shows that the scanner can provide ultrasonic data from deeply located bones with the ultrasound penetrating the trabecular bone up to a depth of 20 mm. It is also shown that the RF echo data acquired with the scanner allow for the estimation of attenuation coefficient and frequency dependence of backscattering coefficient of trabecular bone. The values of the calculated parameters are in the range of corresponding in vitro data from the literature but their variation is relatively high.     

Wavelet transform-based strain estimator for elastography

A new signal processing algorithm based on a wavelet transform (WT) is proposed for instantaneous strain estimation in acoustic elastography. The proposed estimator locally weighs ultrasonic echo signals acquired before tissue compression by a Gaussian window function and uses the resulting waveform as a mother wavelet to calculate the WT of the postcompression signal. From the location of the WT peak, strain is estimated in the time-frequency domain. Because of the additive noise in signals and the discrete sampling, errors are commonly made in estimating the strain. Statistics of these errors are analyzed theoretically to evaluate the performance of the proposed estimator. The strain estimates are found to be unbiased, but error variances depend on the signal properties (echo signal-to-noise ratio and bandwidth), signal processing parameter (time-bandwidth product), and the applied strain. The results are compared with those obtained from the conventional strain estimator based on time-delay estimates. The proposed estimator is shown to offer strain estimates with greater precision and potentially higher spatial resolution, dynamic range, and sensitivity at the expense of increased computation time.     

基于提升小波变换的超声信号消噪技术

为了提高超声无损检测（UNDT）和无损评价（UNDE）中基础数据的信噪比（SNR）,提出了一种基于提升小波变换多分辨率分析的超声信号消噪新技术.在分析传统裂谱分析（SSP）方法原理及其局限性的基础上,通过采用提升小波变换多分辨率分析能力将原始超声回波信号进行子带分解,然后按照一定的信噪分离规则来消除噪声,达到提高信噪比的目的.实验结果表明,与传统裂谱分析方法相比,该方法增强了消噪性能的稳定性,提高了超声回波信号的信噪比.     

基于小波变换的裂谱分析法

 为了提高超声无损检测（UNDT）和无损评价（UNDE）中基础数据的信噪比（SNR）,提出了一种基于小波变换多分辨率分析的裂谱分析新方法．该方法在分析传统裂谱分析（SSP）方法原理及其局限性的基础上,通过采用小波变换多分辨率分析能力将原始超声回波信号进行等Q子带分解,然后按照一定的信噪分离规则来消除噪声,达到提高信噪比的目的．实验结果表明,与传统裂谱分析方法相比,该方法提高了消噪性能的稳定性,增强了湮没晶粒(或其他散射体)散射中的缺陷回波信号能力．     

Bandwidth and resolution enhancement through pulse compression

A novel pulse compression technique is developed that improves the axial resolution of an ultrasonic imaging system and provides a boost in the echo signal-to-noise ratio (eSNR). The new technique, called the resolution enhancement compression (REC) technique, was validated with simulations and experimental measurements. Image quality was examined in terms of three metrics: the eSNR, the bandwidth, and the axial resolution through the modulation transfer function (MTF). Simulations were conducted with a weakly-focused, single-element ultrasound source with a center frequency of 2.25 MHz. Experimental measurements were carried out with a single-element transducer (f/3) with a center frequency of 2.25 MHz from a planar reflector and wire targets. In simulations, axial resolution of the ultrasonic imaging system was almost doubled using the REC technique (0.29 mm) versus conventional pulsing techniques (0.60 mm). The -3 dB pulse/echo bandwidth was more than doubled from 48% to 97%, and maximum range sidelobes were -40 dB. Experimental measurements revealed an improvement in axial resolution using the REC technique (0.31 mm) versus conventional pulsing (0.44 mm). The -3 dB pulse/echo bandwidth was doubled from 56% to 113%, and maximum range sidelobes were observed at -45 dB. In addition, a significant gain in eSNR (9 to 16.2 dB) was achieved.     

Harmonic chirp imaging method for ultrasound contrast agent

Coded excitation is currently used in medical ultrasound to increase signal-to-noise ratio (SNR) and penetration depth. We propose a chirp excitation method for contrast agents using the second harmonic component of the response. This method is based on a compression filter that selectively compresses and extracts the second harmonic component from the received echo signal. Simulations have shown a clear increase in response for chirp excitation over pulse excitation with the same peak amplitude. This was confirmed by two-dimensional (2-D) optical observations of bubble response with a fast framing camera. To evaluate the harmonic compression method, we applied it to simulated bubble echoes, to measured propagation harmonics, and to B-mode scans of a flow phantom and compared it to regular pulse excitation imaging. An increase of approximately 10 dB in SNR was found for chirp excitation. The compression method was found to perform well in terms of resolution. Axial resolution was in all cases within 10% of the axial resolution from pulse excitation. Range side-lobe levels were 30 dB below the main lobe for the simulated bubble echoes and measured propagation harmonics. However, side-lobes were visible in the B-mode contrast images.     

A fundamental limit on delay estimation using partially correlatedspeckle signals

Delay estimation is used in ultrasonic imaging to estimate blood or soft tissue motion, to measure echo arrival time differences for phase aberration correction, and to estimate displacement for tissue elasticity measurements. In each of these applications delay estimation is performed using speckle signals which are at least partially decorrelated relative to one another. Delay estimates which utilize such data are subject to large errors known as false peaks and smaller magnitude errors known as jitter. While false peaks can sometimes be removed through nonlinear processing, jitter errors place a fundamental limit on the performance of delay estimation techniques. The authors apply the Cramer-Rao Lower Bound to derive an analytical expression which predicts the magnitude of jitter errors incurred when estimating delays using radio frequency (RF) data from speckle targets. The analytical expression presented includes the effects of signal decorrelation due to physical processes, corruption by electronic noise, and a number of other factors. Simulation results are presented which show that the performance of the normalized cross correlation algorithm closely matches theoretical predictions. These results indicate that for poor signal to noise ratios (0 dB) a small improvement in signal to noise ratio can dramatically reduce jitter magnitude. At high signal to noise ratios (30 dB) small amounts of signal decorrelation can significantly increase the magnitude of jitter errors     

Complex principal components for robust motion estimation

Bias and variance errors in motion estimation result from electronic noise, decorrelation, aliasing, and inherent algorithm limitations. Unlike most error sources, decorrelation is coherent over time and has the same power spectrum as the signal. Thus, reducing decorrelation is impossible through frequency domain filtering or simple averaging and must be achieved through other methods. In this paper, we present a novel motion estimator, termed the principal component displacement estimator (PCDE), which takes advantage of the signal separation capabilities of principal component analysis (PCA) to reject decorrelation and noise. Furthermore, PCDE only requires the computation of a single principal component, enabling computational speed that is on the same order of magnitude or faster than the commonly used Loupas algorithm. Unlike prior PCA strategies, PCDE uses complex data to generate motion estimates using only a single principal component. The use of complex echo data is critical because it allows for separation of signal components based on motion, which is revealed through phase changes of the complex principal components. PCDE operates on the assumption that the signal component of interest is also the most energetic component in an ensemble of echo data. This assumption holds in most clinical ultrasound environments. However, in environments where electronic noise SNR is less than 0 dB or in blood flow data for which the wall signal dominates the signal from blood flow, the calculation of more than one PC is required to obtain the signal of interest. We simulated synthetic ultrasound data to assess the performance of PCDE over a wide range of imaging conditions and in the presence of decorrelation and additive noise. Under typical ultrasonic elasticity imaging conditions (0.98 signal correlation, 25 dB SNR, 1 sample shift), PCDE decreased estimation bias by more than 10% and standard deviation by more than 30% compared with the Loupas method and normalized cross-correlation with cosine fitting (NC CF). More modest gains were observed relative to spline-based time delay estimation (sTDE). PCDE was also tested on experimental elastography data. Compressions of approximately 1.5% were applied to a CIRS elastography phantom with embedded 10.4-mm-diameter lesions that had moduli contrasts of -9.2, -5.9, and 12.0 dB. The standard deviation of displacement estimates was reduced by at least 67% in homogeneous regions at 35 to 40 mm in depth with respect to estimates produced by Loupas, NC CF, and sTDE. Greater improvements in CNR and displacement standard deviation were observed at larger depths where speckle decorrelation and other noise sources were more significant.     

Echography using correlation techniques: choice of coding signal

Theoretical studies made in the early 1980's suggest that ultrasonic imaging using correlation technique can overcome some of the drawbacks of classical pulse echography. Indeed by transmitting a continuous coded signal and then compressing it into a short, high resolution pulse at the receiver the total signal to noise ratio (SNR) is improved. The target location is determined by cross correlation of the emitted and the received signal. The band compression allows, by increasing SNR, the retrieval of echo signals buried in the receiver noise. Thus in medical-type echography, where the signal attenuation at fixed depth is proportional to the frequency, the SNR improvement allows the use of higher frequency signals and leads to improved resolution. We report here the results of comparative experimental studies of simple echo B type images as obtained by the classical pulse echo and correlation techniques. Because the optimisation of the coded signal plays a crucial role in the performance of the correlation technique we will also present a comparative study of the performances of the most common codes (m-sequences and complementary series). In particular we shall emphasise the following points: the relative importance of the central lobe as compared to the side lobes of the correlation function, which is directly related to the dynamic of the imaging system, the width of the correlation peak which is directly related to the axial resolution of the system, the facility of the realisation. The merit of B-mode images obtained with the coded signals will be discussed showing that as far as signal modulation is used the best results are obtained with periodic m-sequences     

Optimization of buffer rod geometry for ultrasonic sensors with reference path

Several applications of ultrasonic techniques are limited by the signal-to-noise ratio (SNR). Transducers in these applications usually operate in the pulse-echo mode. Many transducers, especially those for high temperatures, use buffer rods. Often a reference path is used to eliminate electrical and transducer drift. Interference of echo signals and noise causes errors of both amplitude and phase measurement of the detected echoes. In this paper we discuss the influence of major noise sources as a function of geometry and operating environment. The effects are studied using both experimental results and models. Although the results are applied to an ultrasonic density sensor operating in the pulse-echo mode, they are applicable to other pulse-echo mode transducers comprising homogeneous cylindrical buffer rods. This paper will show how the SNR of the density transducer was improved in a special time window from 34 to 72 dB by careful design.     

Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.     

基于EEMD和低秩稀疏分解的超声缺陷回波检测方法

针对应用超声对金属材料微小缺陷检测时缺陷回波容易被噪声干扰的问题,提出了一种基于集合经验模态分解(EEMD)和低秩稀疏分解相结合的检测方法,以避免传统基于经验模态分解(EMD)的去噪方法难以消除结构噪声的问题.首先对缺陷检测信号进行EEMD得到一系列本征模态函数(IMF),采用基于概率密度函数的相似性测量方法选取相关模...