A method for nonlinearity compensation of OFDR based on polynomial regression algorithm

A method based on polynomial regression algorithm(PRA) is proposed in this paper to compensate the nonlinear phase noise in optical frequency domain reflection(OFDR) systems. In this method, the nonlinear phase of OFDR systems is represented by the polynomial phase function, and then the coefficients of the polynomial phase function are estimated by PRA. Finally, the nonlinearity is compensated by match Fourier transform(MFT). Simulation results demonstrate that the proposed algorithm has good performance in compensating both weak and strong nonlinear phase noises of OFDR systems.     

Motion-induced phase error estimation and correction in 3D diffusion tensor imaging

A multishot data acquisition strategy is one way to mitigate B0 distortion and T2? blurring for high-resolution diffusion-weighted magnetic resonance imaging experiments. However, different object motions that take place during different shots cause phase inconsistencies in the data, leading to significant image artifacts. This work proposes a maximum likelihood estimation and k-space correction of motion-induced phase errors in 3D multishot diffusion tensor imaging. The proposed error estimation is robust, unbiased, and approaches the Cramer-Rao lower bound. For rigid body motion, the proposed correction effectively removes motion-induced phase errors regardless of the k-space trajectory used and gives comparable performance to the more computationally expensive 3D iterative nonlinear phase error correction method. The method has been extended to handle multichannel data collected using phased-array coils. Simulation and in vivo data are shown to demonstrate the performance of the method.     

飞秒激光合成波长法测距的功率-相位转换误差修正研究

针对飞秒激光合成波长法高精度绝对距离测量中光功率-相位转换效应引起的误差,提出一种基于多项式拟合的误差修正方法,以提高飞秒激光测量系统的测距精度。搭建类迈克耳孙干涉测量系统,经过光电探测后得到飞秒激光模间拍频信号,利用快速傅里叶变换解算拍频信号的相位差,并研究相位差随光功率的变化。结合相位测距技术,将测距结果与长度基准作参考,采用基于最小二乘法的最优多项式拟合形成不同光功率下的测距校正表。实验中以四次谐波进行测量,结果表明:当光功率在1~3 mW变化时,测距误差变化率约为2.7 mm/mW,通过校正技术,在110 mm范围内测距残余误差从±0.25 mm下降到±0.08 mm。该研究可将飞秒激光高精度测距技术应用到室外环境、复杂的工业环境甚至非合作目标等光功率变化较大的测量场合,显著地拓展飞秒激光精密测量的应用范围。     

Parametric estimate of intensity inhomogeneities applied to MRI

This paper presents a new approach to the correction of intensity inhomogeneities in magnetic resonance imaging (MRI) that significantly improves intensity-based tissue segmentation. The distortion of the image brightness values by a low-frequency bias field impedes visual inspection and segmentation. The new correction method called parametric bias field correction (PABIC) is based on a simplified model of the imaging process, a parametric model of tissue class statistics, and a polynomial model of the inhomogeneity field. We assume that the image is composed of pixels assigned to a small number of categories with a priori known statistics. Further we assume that the image is corrupted by noise and a low-frequency inhomogeneity field. The estimation of the parametric bias field is formulated as a nonlinear energy minimization problem using an evolution strategy (ES). The resulting bias field is independent of the image region configurations and thus overcomes limitations of methods based on homomorphic filtering. Furthermore, PABIC can correct bias distortions much larger than the image contrast. Input parameters are the intensity statistics of the classes and the degree of the polynomial function. The polynomial approach combines bias correction with histogram adjustment, making it well suited for normalizing the intensity histogram of datasets from serial studies. We present simulations and a quantitative validation with phantom and test images. A large number of MR image data acquired with breast, surface, and head coils, both in two dimensions and three dimensions, have been processed and demonstrate the versatility and robustness of this new bias correction scheme.     

A parametric method for non-stationary interference suppression in direct sequence spread-spectrum systems

The problem of non-stationary interference suppression in direct sequence spread-spectrum (DS-SS) systems is considered. The phase of interference is approximated by a polynomial within the considered interval. According to the local polynomial Fourier transform (LPFT) principle, the received signal is dechirped by using the obtained phase approximation and the interference is, in turn, suppressed by excising the corrupted low-pass frequency band. For the estimation of polynomial coefficients, we use the product high-order ambiguity function (PHAF), known for its capability to successfully resolve components of a multicomponent polynomial-phase signal (PPS). The proposed method can suppress interferences with both polynomial and non-polynomial phase. In addition, it can suppress both monocomponent and multicomponent interferences. The simulations show that the proposed method outperforms time-frequency (TF) methods, that successfully deal with multicomponent interferences, in terms of the error probability and computational complexity.     

Polynomial-Approximation-Based Control for Nonlinear Systems

This paper is concerned with the stabilization problem for nonlinear systems. A new polynomial-approximation-based approach for modeling nonlinear systems is first proposed. The nonlinearity is approximated by polynomials, and the approximation errors are treated as modeling uncertainties. The original nonlinear systems are converted into polynomial systems with modeling uncertainties. In order to highlight the approximation accuracy, the piecewise polynomial approximation functions are utilized. A novel polynomial state-feedback controller is designed to solve the stabilization problem. Furthermore, switched polynomial state-feedback controllers are designed to improve the performance. The stabilization conditions are presented in terms of sum of squares, which can be numerically solved via SOSTOOLS. Finally, simulation examples are provided to demonstrate the feasibility of the proposed method and show its advantage over the polynomial-fuzzy-model-based approach.     

MRI artifact cancellation due to rigid motion in the imaging plane

A post-processing technique has been developed to suppress the magnetic resonance imaging (MRI) artifact arising from object planar rigid motion. In two-dimensional Fourier transform (2-DFT) MRI, rotational and translational motions of the target during magnetic resonance magnetic resonance (MR) scan respectively impose nonuniform sampling and a phase error an the collected MRI signal. The artifact correction method introduced considers the following three conditions: (1) for planar rigid motion with known parameters, a reconstruction algorithm based on bilinear interpolation and the super-position method is employed to remove the MRI artifact, (2) for planar rigid motion with known rotation angle and unknown translational motion (including an unknown rotation center), first, a super-position bilinear interpolation algorithm is used to eliminate artifact due to rotation about the center of the imaging plane, following which a phase correction algorithm is applied to reduce the remaining phase error of the MRI signal, and (3) to estimate unknown parameters of a rigid motion, a minimum energy method is proposed which utilizes the fact that planar rigid motion increases the measured energy of an ideal MR image outside the boundary of the imaging object; by using this property all unknown parameters of a typical rigid motion are accurately estimated in the presence of noise. To confirm the feasibility of employing the proposed method in a clinical setting, the technique was used to reduce unknown rigid motion artifact arising from the head movements of two volunteers.     

Polynomial phase signal analysis based on the polynomialderivatives decompositions

An exact decomposition of the derivatives of any order of a polynomial φ(t) is proposed in terms of φ(t-t₀), ..., φ(t-t_n). This result allows us to introduce generalized time-frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase. The relationships between these distributions and the already known polynomial distributions, i.e., the polynomial phase transform and the polynomial Wigner-Ville distribution, are discussed. Illustrations by example are proposed     

近距离超宽带调频连续波雷达非线性校正研究

调频连续波雷达凭借其结构简单、造价低廉等优势在目标探测与识别等方面体现出重要的应用价值,然而系统的非线性调制问题成为制约其性能的重要因素。传统的非线性校正方法能够在一定程度上估计非线性,但估计过程中的误差传递问题导致校正效果并不理想。基于该问题,本文提出一种基于多项式回归的方法实现非线性的准确估计。所提算法首先将非线性相位建模为多项式函数,然后通过多项式回归实现参数的联合估计,以消除误差传递问题。基于估计出的参数,通过时域重采样操作实现非线性的校正。仿真结果表明,所提算法不仅能够准确估计出多项式参数,而且在一定信噪比下比传统算法更接近克拉美—罗界。X波段FMCW雷达实测数据处理结果显示,本文所提算法可以有效消除非线性误差。      

Automated model-based bias field correction of MR images of the brain

We propose a model-based method for fully automated bias field correction of MR brain images. The MR signal is modeled as a realization of a random process with a parametric probability distribution that is corrupted by a smooth polynomial inhomogeneity or bias field. The method we propose applies an iterative expectation-maximization (EM) strategy that interleaves pixel classification with estimation of class distribution and bias field parameters, improving the likelihood of the model parameters at each iteration. The algorithm, which can handle multichannel data and slice-by-slice constant intensity offsets, is initialized with information from a digital brain atlas about the a priori expected location of tissue classes. This allows full automation of the method without need for user interaction, yielding more objective and reproducible results. We have validated the bias correction algorithm on simulated data and we illustrate its performance on various MR images with important field inhomogeneities. We also relate the proposed algorithm to other bias correction algorithms.