Modified fringe-adjusted joint transform correlation to accommodate noise in the input scene

A modified fringe-adjusted joint transform correlator is proposed that is able to accommodate noise in the input scene. The effect of noise in the input scene on the performance of the joint transform correlator is analyzed and quantified. When the target is embeddedin aseverely noise-corrupted input scene, it is shown that the proposed modified fringe-adjusted filter joint transform correlator delivers a better correlation performance and the capacity to accommodate this noise than does the fringe-adjusted filter-based correlator. When the power spectra of the input image and the reference image are subtracted from the power spectrum of the joint-input image, it is found that the noise effect on the output plane is independent of the objects in the input scene and originates from the convolution of the reference image and noise in the input scene.     

Multiple-target detection with use of a modified amplitude-modulated joint transform correlator

Multiple-target detection with a modified amplitude-modulated joint transform correlator is proposed. With this technique the joint power spectrum is first modified by the subtraction of the power spectrum of the input scene only and of the reference image from it; the resultant modified joint power spectrum is next multiplied by the amplitude-modulated filter function. The effect of noise in the input scene on the performance of the joint transform correlator is analyzed and quantified. This technique is found to deliver a correlation output and the capacity to accommodate noise in the input scene better than both the fringe-adjusted filter-based joint transform correlator and the modified fringe-adjusted filter-based joint transform correlator.     

Estimation of mean frequency and variance of ultrasonic Doppler signal by using second-order autoregressive model

In order to estimate the mean frequency and variance of the diagnostic ultrasound Doppler signal in the presence of clutter noise, a new estimator using a second-order autoregressive (AR) model, called the AR estimator, is proposed. The sampled signal that contains information of both the Doppler signal and clutter is described by the second-order AR model with two poles. The mean frequency and variance of a unidirectional Doppler signal can be estimated, respectively, from the phase and the magnitude of the pole, with larger phase between the two poles. If the clutter is not completely rejected, all conventional estimators, including the autocorrelation (AC) estimator, result in erroneous estimations for the mean frequency and variance of the Doppler signal, whereas the AR estimator gives an accurate estimation. In the absence of clutter, however, the performance of both the AC and AR estimators are similar. If the blood flows in both directions in a sample volume and the clutter is rejected to the extent that it no longer obscures the Doppler signal, the proposed method can estimate simultaneously the mean frequencies and variances of both the forward and reverse blood flows. The performance of the proposed AR estimator was compared with that of the AC estimator by computer simulations and experiments, and it was found that when the number of available sampled data is small, the AR estimator does not require the use of a clutter filter, which simplifies Doppler signal detection.     

A comparison of two correlation schemes

Processes involving the cross-correlation of two noisy data streams are frequently encountered in signal processing. The performances of two commonly used correlators, the simple and complex correlators, are examined. The conventional view is that the complex correlator is superior to the simple correlator by a factor of the square root of two in output signal-to-noise ratio (SNR). However, by modifying the simple correlator to utilize all the available information, its performance is improved. The development of the modified correlator is explained, and a computer simulation shows that this modified correlator is approximately equivalent to the complex correlator in noise performance     

基于液晶光阀微分处理的实时联合变换相关器

提出了一种用液晶光阀实现对输入图像的微分预处理和对功率谱微分处理的实时联合变换相关器。两个液晶光阀均处于非线性变换态,分别在输入面和频谱面上实现对输入图像和联合功率谱的微分处理。微分功率谱经傅里叶透镜变换后得到相关输出。实验表明,该相关器采用全光方式不仅保证了实时性,而且锐化了相关峰;经该相关器微分后的图像,其相关性能明显优于常规联合变换相关器输出的结果。     

Enhancement of Signal-to-Noise Ratio of Turbulence Measurements by Cross Correlation

A novel method for the measurement of very low turbulence intensities in fluids, based on a dual heat-transfer transducer and a cross correlator, is described. The minimum measurable turbulence intensity is shown to vary with the square root of the minimum detectable cross-correlation coefficient ?. The effects of finite additive noise correlation and finite lateral separation between the transducer halves are studied. Details are given of an instrument measuring the normalized cross-correlation coefficient between two time-dependent signals in the frequency range 2 Hz-300 kHz with an accuracy of ±0.05? ±0.01. The described correlator is particularly suitable for measurements of quasi-stationary processes. A variation of 10 percent in the level of either input signal results in a correlation error of less than 0.6 percent.     

Generalized joint fractional fourier transform correlators: a compact approach

Fractional correlation was introduced recently. We generalize the architecture of a joint (Fourier) transform correlator (JTC) to achieve the joint fractional (Fourier) transform correlator (JFrTC) such that fractional correlation can be obtained. Here the Fourier transform in the JTC is replaced by the fractional Fourier transform, and four different JFrTC architectures can be implemented. The mathematical derivations for these JFrTC architectures are given, together with the simulation verifications. The JFrTC can provide a correlation signal similar to a delta function but with a small discrimination ratio, such that it is insensitive to additive noise. In a conventional JTC the distance between the two desired correlation signals at the output plane is fixed and depends on the distance between the input and the reference signals. However, with a given fractional order and an additional phase mask the separation distance between the two correlation signals at the output plane of a JFrTC can be larger or smaller than that of a JTC. This property is useful for the applications of real-time target tracking. Unlike in a previous approach [Appl. Opt. 36, 7402 (1997)], we need only two fractional Fourier transformations instead of three to achieve fractional correlation.     

Fourier-plane windowing in the binary joint transform correlator for multiple target detection

With recent advances in state-of-the-art spatial light modulators, the optical joint transform correlator (JTC) and the binary joint transform correlator (BJTC) are becoming practical signal-processing tools. The performance of these devices is limited by the difficulty of separating the cross correlation between the reference and the targets in the scene from signals resulting from cross correlations between objects in the target scene. One technique that reduces this problem is to use a sliding window in the Fourier plane as a convolution mask filter to set an adaptive binarization threshold. This suppresses the autocorrelation response and reduces the dynamic range of the Fourier-plane signal. This results in correlation performance improvement by a factor of 2 to 4. A mathematical model is developed to describe the windowing process for both the JTC and BJTC for the case in which the scene contains multiple targets and background clutter. The derivation of the windowing process is general and includes any spatial high-pass or bandpass filtering in the Fourier plane. The results are supported with experimental data.     

Quantization error in processing the signal from a laser Doppler anemometer

The effect of quantization noise arising in the course of digital processing of the signal of a laser Doppler anemometer on the error in Doppler signal frequency estimation in the time domain is considered. It is shown that in high-precision measurements the quantization noise that appears in amplitude quantization of the signal of a laser Doppler anemometer is comparable with other noise sources and must be taken into account in estimation of the limiting accuracy of a laser Doppler anemometer. Results of a simulation and experiment are presented. Translated from Izmeritel'naya Tekhnika, No. 9, pp. 15–17, September. 1998.     

Approximate performance of the nonlinear joint transform correlator in signallike noise

We present a statistical-analysis technique for a nonlinear joint transform correlator (JTC) based on two assumptions: the noise and the signal spectra are identical, and the signal energy is small relative to the noise energy. The first assumption, while admittedly convenient, is also defensible in that it is a worst case and in that image and scene noise can be similar in texture. The second is also reasonable, given that even a clearly visible signal may have small energy compared with the scene noise if it is of limited extent; in any case, the results appear moderately faithful even for the case that signal and noise energies are equal. We discover that the optimal Fourier-plane transformation is spatially variant and tends to remove the Fourier amplitudes of the input image, and indeed functions in a way very similar to the spatially variant binary JTC. We also see that the classic (or spatially invariant linear) JTC is a very inferior technique for signallike noise, that the best spatially variant binary JTC uses a threshold proportional to the noise power spectrum, and that, if a spatially invariant binary-thresholded JTC is desired, then the median Fourier-plane value is an excellent choice of threshold. The performance predictions are verified by simulation and appear to be reasonable even for the highly nonlinear binary schemes.     

Analysis of spatial light modulator contrast ratios and optical correlation

We have performed a general analysis of optical correlators with spatal light modulators (SLM's) whose primary defect is a finite contrast ratio (CR). Our mathematical analysis identifies three noise terms that appear in addition to the correlation term. The filter SLM contains either a phase-only filter (POF) or a binary-phase-only filter (BPOF). Insertion of a dc block at the center of the filter SLM decreases the noise background in the correlator plane; this dc block is larger than that required for the same level of performance in a correlator whose SLM's have transmissive (or reflective) dead zones. With a noise-free input and the dc block, our computer simulations that show the peak intensity falling off as the CR decreases are in quantitative agreement with the correlation term of the mathematical model. For a cluttered, disjoint noise input this agreement is only qualitative, and at low CR's the dc block is definitely required for the BPOF correlator if the secondary peaks in the output are to be brought below the correlation peak.     

Calibration method for inner product calculation by the volume holographic correlator with randomly interleaved images

A volume holographic correlator is capable of inner product calculations between the input image and multiple stored images in parallel. The inner product that is the center value of the correlation can provide a scalar measure of change between two images. The inner product values are directly acquired by measuring the intensities of the correlation peaks on the CCD. However, the measured intensities are not exactly equal to the theoretical inner product values due to the redundancy correlation. The structure of the correlation peak for randomly interleaved images is analyzed. It can be regarded as two volumes, one pyramid and one prism. The relative inner product value is only determined by the height of the pyramid. The prism, caused by the redundancy correlation, appears as the background noise, which is the main source of the inner product calculation error. A calibration method is proposed to remove the prism from the measured intensity. Based on the geometric structure of the correlation peak, the theoretical expression of the inner product value for the pyramid is derived. A white image is employed as the input image and the measured correlation peak intensity is used to calibrate the inner product value. The calibration method can effectively eliminate the error caused by the redundancy correlation to achieve a high output accuracy of the volume holographic correlator. Experiments are demonstrated for the validity of the method.     

In-line interferometric time-integrating acousto-optic correlator

A novel, efficient, stable, in-line interferometric, two Bragg cell, acousto-optic architecture is introduced for signal correlation and spectrum analysis. The processor employs an image-inversion technique to produce a correlation output that does not have to be generated on a fast spatial carrier, thus reducing the burden on the required space-bandwidth product on the output time-integrating detector array. The system is particularly suited for wide-instantaneous-bandwidth signal processing and is demonstrated as an autocorrelator for dc-to-10-MHz AM signals on a 100-MHz carrier. A fixed-spatial-carrier outputbased correlator and spectrum-analyzer architecture that is particularly limited in the wideband mode is demonstrated for comparison purposes with the proposed flexible-spatial-carrier-design-based in-line acousto-optic correlator.     

A new time-domain narrowband velocity estimation technique for Doppler ultrasound flow imaging. II. Comparative performance assessment

For pt.I see ibid., vol.45, no.4, pp.939-54 (1998). The statistical performance of the new 2-D narrowband time-domain root-MUSIC blood velocity estimator described previously is evaluated using both simulated and flow phantom wideband (50% fractional bandwidth) ultrasonic data. Comparisons are made with the standard 1-D Kasai estimator and two other wideband strategies: the time domain correlator and the wideband point maximum likelihood estimator. A special case of the root-MUSIC, the "spatial" Kasai, is also considered. Simulation and flow phantom results indicate that the root-MUSIC blood velocity estimator displays a superior ability to reconstruct spatial blood velocity information under a wide range of operating conditions. The root-MUSIC mode velocity estimator can be extended to effectively remove the clutter component from the sample volume data. A bimodal velocity estimator is formed by processing the signal subspace spanned by the eigenvectors corresponding to the two largest eigenvalues of the Doppler correlation matrix. To test this scheme, in vivo common carotid flow complex Doppler data was obtained from a commercially available color flow imaging system. Velocity estimates were made using a reduced form of this data corresponding to higher frame rates. The extended root-MUSIC approach was found to produce superior results when compared to both 1- and 2-D Kasai-type estimators that used initialized clutter filters. The results obtained using simulated, flow phantom, and in vivo data suggest that increased sensitivity as well as effective clutter suppression can be achieved using the root-MUSIC technique, and this may be particularly important for wideband high frame rate imaging applications.     

抗噪性联合变换相关器

我们对联合变换相关器的输入图象进行Roberts梯度处理,同时对参考图象采取相移技术,并在频域中将功率谱二值化。与传统的联合变换相关器（CJTC）相比,新型的联合变换相关器（NJTC）消除了功率谱的直流分量,锐化了相关峰强度,提高了衍射效率和识别能力,同时增强了联合变换相关器的抗噪性能。用计算机模拟出预言结果。     

On the performance of regression and step-initialized IIR clutterfilters for color Doppler systems in diagnostic medical ultrasound

One of the major issues in color Doppler ultrasound is the suppression of clutter that arises from stationary or slowly moving tissue. If not adequately suppressed, clutter can severely affect the ability of color Doppler systems to accurately estimate the Doppler mean frequency and power of blood, resulting in a potentially misleading depiction of flow. In this study, the performances of two classes of clutter suppression techniques-step-initialized infinite impulse response (IIR) and regression filters-were evaluated and compared by means of extensive simulations. The performance indicators used were the accuracy and precision of the mean frequency and the power estimates after clutter filtering. In summary, the ability of both filter classes to suppress clutter was found to vary considerably depending on factors such as the clutter-to-flow-signal ratio and the ensemble length. In particular, the performance of step-initialized IIR filters was shown to be noticeably inferior to that predicted by their steady-state response. Regression filters were found to offer significantly better performance than step-initialized IIR filters under heavy clutter conditions and, given their steeper roll-off, appear to be more effective clutter suppressors for power Doppler imaging. However, it should be noted that, as demonstrated by the simulations, the performance of IIR filters is severely degraded by their transient response which, in turn, is determined by the initialization scheme used. Therefore, more elaborate schemes-with superior transient characteristics than step-initialization-could significantly improve the effectiveness of IIR filtering under heavy clutter conditions     

Robustification of noise radar detection

A study of robust detection scheme for continuous wave noise radars is presented. The probability density function (PDF) of the noise at the input of the radar is not usually Gaussian and has heavy tails generated by impulse interferences. Although the PDF of interferences at the output of the noise radar correlator is Gaussian, impulse interferences increase the processing floor, and thus decrease the overall radar sensitivity. The proposed robustification applied to the correlator?s input signal increases the radar sensitivity in the presence of impulse interferences, and does not introduce any significant losses if the input noise is purely Gaussian.     

Fractional correlation operation: performance analysis

The fractional correlation is a new tool related to the fractional Fourier transform. It is useful for comparison and recognition, especially for shift-variant cases. The performances of such a correlator are analyzed according to the standard criteria of signal-to-noise ratio, correlation sharpness (peak-to-correlation energy), and Horner efficiency. The conclusions are that the performance is object dependent and that for nonwhite noise, compared with the conventional correlator, improved performances are possible. In addition we show that for a white-noise spectrum the fractional correlation has performances similar to the conventional correlator.     

Speckle velocimetry by means of holographic time-integrative correlation

We develop the theory of the speckle velocimeter that is based on use of a photorefractive real-time hologram in four-wave mixing as a time-integrative correlator. The theory of the speckle velocimeter has been developed for the time correlation between the far-field spectrum of light scattered from the diffuser and the reference wave that is Doppler shifted. Our theoretical derivation shows that it is possible to extract the velocity with minor processing of the output correlation.