Phase Local Approximation (PhaseLa) Technique for Phase Unwrap From Noisy Data

The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (ICI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval (-pi,pi) and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the ICI adaptation algorithm.     

A spatially adaptive nonparametric regression image deblurring.

We propose a novel nonparametric regression metthod for deblurring noisy images. The method is based on the local polynomial approximation (LPA) of the image and the paradigm of intersecting confidence intervals (ICI) that is applied to define the adaptive varying scales (window sizes) of the LPA estimators. The LPA-ICI algorithm is nonlinear and spatially adaptive with respect to smoothness and irregularities of the image corrupted by additive noise. Multiresolution wavelet algorithms produce estimates which are combined from different scale projections. In contrast to them, the proposed ICI algorithm gives a varying scale adaptive estimate defining a single best scale for each pixel. In the new algorithm, the actual filtering is performed in signal domain while frequency domain Fourier transform operations are applied only for calculation of convolutions. The regularized inverse and Wiener inverse filters serve as deblurring operators used jointly with the LPA-design directional kernel filters. Experiments demonstrate the state-of-art performance of the new estimators which visually and quantitatively outperform some of the best existing methods.     

The ZπM algorithm: a method for interferometric imagereconstruction in SAR/SAS

This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.     

Amplitude estimation of rectangular narrow-band radio pulse with unknown duration and initial phase

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.     

瞬时频率引导的小波变换轮廓术相位解包裹技术

提出了一种新的用于小波变换轮廓术进行相位解 包裹的质量图建立方法。对受物体形貌调制的变形 条纹图,利用小波变换相位解调技术获得变形条纹的包裹相位与瞬时频率;将瞬时频率与条 纹载频的绝对 差值和相邻像素点之间瞬时频率的变化程度两方面建立质量图,质量图值的大小可表示位 相质量的好坏, 质量图的值越小,相位质量越可靠;再设定阈值,将质量图分为质量好坏两部分,不同 部分分别采用 扫描线算法和洪流相位解包裹法进行位相解包裹。本文方法在提高解包裹处理速度的同时, 还可以更为精确 地检测出噪声、阴影或条纹突变等区域,使相位解包裹精度和效率得到了保证。通过理论分 析、仿真分析、 实物静态和动态实验表明,与现有的质量图引导的洪流相位解包裹法 相比,本文方法解包裹速 度更快,适用于动态测量中大量变形条纹图的相位精确快速解包裹。     

Phase regression approach for estimating the parameters of a noisy multifrequency signal

A novel approach for estimating the parameters of a multifrequency signal from discrete samples corrupted by additive noise is presented. An established mathematical model indicates that noise influence on the discrete phase and amplitude spectra is equivalent to additive phase and amplitude noise, respectively. On this basis, a simple algorithm is proposed to estimate the frequency and phase of each sinusoid component by linear regression on the phase spectra of segmented signal blocks, while an amplitude estimator is directly derived from the spectrum of the window function. The circular nature of the phase spectrum is thoroughly explored. Also, an algorithmic scheme is presented. The derived variances of the estimators show that for a noisy signal this approach provides superior accuracy over the traditional approaches. Simulations and engineering application confirm the validity of the presented method.     

基于自适应滤波器的相位连续化算法及其在移相干涉术中的应用

提出一种非线性自适应数字滤波器对通过移相干涉术得到的原理相位图进行去噪音处理。这种数字滤波器的窗口尺寸可以根据其在相位图中的不同位置而变化。在有噪音 (尤其是靠近 2π相位跳变处的噪音 )存在的情况下 ,相位连续化过程仍可以有效地进行以重建被测物体表面形貌的真实相位图。详细介绍了这一技术的原理及实验结果     

The Wigner distribution of noisy signals with adaptivetime-frequency varying window

Time-frequency representations using the Wigner distribution (WD) may be significantly obscured by the noise in the observations. The analysis performed for the WD of discrete-time noisy signals shows that this time-frequency representation can be optimized by the appropriate choice of the window length. However, the practical value of this analysis is not significant because the optimization requires knowledge of the bias, which depends on the unknown derivatives of the WD. A simple adaptive algorithm for the efficient time-frequency representation of noisy signals is developed in this paper. The algorithm uses only the noisy estimate of the WD and the analytical formula for the variance of this estimate. The quality of this adaptive algorithm is close to the one that could be achieved by the algorithm with the optimal window length, provided that the WD derivatives were known in advance. The proposed algorithm is based on the idea that has been developed in our previous work for the instantaneous frequency (IF) estimation. Here, a direct addressing to the WD itself, rather than to the instantaneous frequency, resulted in a time and frequency varying window length and showed that the assumption of small noise and bias is no longer necessary. A simplified version of the algorithm, using only two different window lengths, is presented. It is shown that the procedure developed for the adaptive window length selection can be generalized for application on multicomponent signals with any distribution from the Cohen (1989, 1990, 1992) class. Simulations show that the developed algorithms are efficient, even for a very low value of the signal-to-noise ratio     

三种基于路径跟踪的位相解包裹算法比较

为了快速准确的对含有噪声和欠采样问题包裹位相图进行位相展开,本文采用理论分析与计算机模拟及实验验证相结合的方法,对基于路径跟踪算法的枝切法(BC)、质量导向的路径跟踪算法(QG)和菱形算法(RA)三种位相解包裹算法作了对比研究。结果表明:RA算法运行速度最快,BC算法次之,QG算法速度最慢;其中BC和RA算法对含有强噪声和欠采样的包裹位相图处理效果较差,QG算法效果相对较好,但这种算法运行的时间较长,不太适合处理实时性要求较高的问题。所以要根据具体实际问题对噪声、欠采样和实时性的不同要求来选取合适的算法。     

Unbiased estimates for on-line system identification

An algorithm is derived for the determination of several unbiased estimates of the parameter vector of a discrete-time system, even in the presence of considerable noise, and requiring only one matrix inversion. From these noisy estimates an improved estimate can then be used by using stochastic approximation.     

FFT Performance in the Presence of Noise

Contamination of signals by noise degrades the performance of fast Fourier transform (FFT) analysis of biological systems. Thus, we have developed simulation techniques to investigate the effects of noise on FFT computations. Continuous and discrete representations of forcing-noise and response-noise signals are derived. The FFT is used to estimate magnitude and phase of noisy digital signals constructed using the discrete representations. The estimates are then compared to the estimates obtained from the noise-free digital signals. The following factors are shown to have an important influence on estimation accuracy: the inclusion of noninteger as well as integer harmonic noise, the signal series length, the relative noise-to-forcing and response signal magnitude ratios, and the degree of noise signal cross correlation between the forcing and response signals. We demonstrate that the FFT estimation accuracy of magnitude and phase is similar for integer and noninteger noise harmonics, it varies directly with signal series length, and inversely with the noise-to-forcing and response signal magnitude ratios.     

Parametric estimation of the orientation of textured planarsurfaces

This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single, noisy, observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Assuming the estimated polynomial coefficients are the coefficients of a Taylor series expansion of the phase, we establish a linear recursive relation between the model parameters and the unknown slant and tilt. A linear least squares solution of the resulting system provides the slant and tilt estimates. To improve accuracy, an iterative refinement procedure is applied in a small neighborhood of these estimates. The performance of the proposed algorithms is evaluated by applying them to images of different planar surfaces, and by comparing their statistical performance with the Cramer-Rao bound. The combined two-stage algorithm is shown to produce estimates that are close to the bound.     

Goldstein枝切法对存在间断相位缺陷的解缠研究

Goldstein枝切法作为相位解缠中路径积分法的重要算法之一,其解缠结果易受到噪声或间断相位缺陷所引起的残差点影响。为了研究相位间断缺陷对解缠算法的影响,模拟了具有间断相位缺陷的数据,采用Goldstein枝切法进行了系统的解缠研究。重点研究了残差点对枝切线的搜索窗口半径大小的影响,并将解缠相位与真实相位进行了比较。结果表明,在单相位间断和双不相交的相位间断缺陷的情况下,Goldstein枝切法仍然具有较好的解缠效果;对于双交叉相位间断缺陷,Goldstein枝切法在这一局部区域无法得到正确的解缠结果;通过研究枝切线搜索窗口半径对解缠的影响,验证了存在“有效枝切线搜索窗口半径”的结论。此实验结果对于采用或联合采用Goldstein枝切法进行的相位解缠理论研究和应用具有参考价值。     

A moment-based variational approach to tomographic reconstruction

We describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood (ML) estimates of its orthogonal moments. We show how these estimated moments and their (correlated) error statistics can be computed directly, and in a linear fashion from given noisy and possibly sparse projection data. Moreover, thanks to the consistency properties of the Radon transform, this two-step approach (moment estimation followed by image reconstruction) can be viewed as a statistically optimal procedure. Furthermore, by focusing on the important role played by the moments of projection data, we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments. Taking advantage of this connection, our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data. We show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem. We show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back-projection (FBP) algorithm.     

Bayesian approaches to phase unwrapping: theoretical study

The problem of phase unwrapping of two-dimensional (2-D) phase signals has gained a considerable interest. It deals with the problem of estimating (reconstructing) an absolute phase from the observation of its noisy principal (wrapped) values. This is an ill-posed problem since many possible solutions correspond to a given observation. Many phase unwrapping algorithms have been proposed relying on different constraints for the phase signal sampling process or the nature (e.g., smoothness, regularity) of the phase signal. We look at these algorithms from the Bayesian point of view (estimation theory) and analyze the role of the prior assumptions, studying their equivalencies to the regularization constraints already used. This study leads to the development of the two new phase unwrapping algorithms which are able to work in quite difficult conditions of aliasing and noise. The theoretical study of the analyzed schemes is illustrated by some experiments on synthetic phase signals     

横向剪切最小二乘相位解包裹算法的改进

对存在欠采样的包裹相位进行解包裹一直是一个难点,尽管横向剪切最小二乘相位解包裹算法有不错的抗欠采样能力,但当存在严重欠采样时,该算法还是不能得到令人满意的结果。针对这个问题作了分析,并通过引入二次剪切的方法改进了横向剪切最小二乘相位解包裹算法,通过模拟计算和实验验证,证明改进后的算法是正确和有效的,该算法可以保证当包裹相位二阶离散导数的绝对值不大于π时能得到正确的解包裹结果。     

一种基于滑动窗能量检测的OFDM符号同步算法

文章提出了一种基于滑动窗能量检测来实现OFDM符号定时同步的算法。为了避免码间干扰（ISI）,通常在帧的起始位置添加保护间隔。该算法正是利用该保护间隔信号能量最小的特点来寻找符号定时同步点。该算法分为粗同步和细同步,通过改变滑动窗的长度,两次寻求滑动窗内信号能量的最小值,来确定最佳的符号定时起点。文中给出了算法的具体步骤。仿真结果表明,该算法具有良好的估计精度。     

基于短时能量的语音端点检测算法研究

研究了噪声环境下，利用短时能量为特征进行语音端点检测的问题。在采用短时全带能量为特征的基础上，提出的算法将短时高频能量作为辅助特征，同时使用了最优边沿检测滤波以及双门限-三态转换判决机制，从而保证了算法在噪声环境下的端点检测准确性和对信号绝对幅度变化的稳健性。实验结果表明，与传统的能量闻值法以及G．729中使用的VAD算法相比，提出的算法在噪声环境下具有更好的性能，是一个简单、高效和稳健的语音端点检测算法。     

Performance Monitoring of Digital Communication Systems Using Extreme-Value Theory

Extreme-value theory has been suggested by various investigators as an efficient tool for use in monitoring the performance of digital communication systems. One drawback to such a procedure is that it requires learning periods to estimate certain parameters of the extremal distributions. Clearly, whenever an update of the estimates is needed, transmission of information must temporarily cease since a new learning period must begin. To avoid this problem, a technique is proposed for obtaining estimates of the parameters when the learning period is eliminated (i.e., estimates are obtained using noisy samples), and these parameter estimates are in turn used to estimate the probability of error of the communication system. The accuracy of this procedure is tested by computer simulation, and it is indicated how one can verify (in a statistical sense) whether or not this technique is appropriate for any given system.     

基于学习的光栅图像噪声抑制方法

基于条纹投影的三维形貌测量广泛应用于工业制造、质量检测、生物医疗、航空航天等领域。然而在高速测量的场景下,由于光栅图像的采集过程曝光时间短,三维重建结果通常会受到较为严重的图像噪声干扰。近年来,深度学习技术在计算机视觉等领域得到了广泛应用,并且取得了巨大的成功。受此启发,提出了一种基于学习的光栅图像噪声抑制方法。首先构建了一个基于U-net的卷积神经网络。其次在训练过程中,构建的神经网络学习从含有噪声的条纹图像到对应高质量包裹相位之间的映射关系。当经过适当训练,该网络可从含有噪声的条纹图像中准确恢复相位信息。实验结果表明:针对离线的快速运动场景三维测量,该方法仅利用一幅光栅图像可恢复高精度的相位信息,且相位精度优于传统的三步相移方法。该方法可为提升运动高速场景三维测量的精度提供切实可靠的解决方案。