Analysis of linear prediction by matrix approximation

The authors present a new method of analysis of the effects of data perturbations on the estimates of signal parameters which are obtained by the method of linear prediction. The variances of signal-parameter obtained from linear prediction methods are computed. Although the results appear to have wide applicability, for simplicity the authors restrict their examples to signals which are linear combinations of complex-valued exponential functions     

Superresolution frequency estimation by alternating notchperiodogram

A novel periodogram-based maximum-likelihood algorithm is proposed for a frequency estimation problem. It is called an alternating notch-periodogram algorithm (ANPA), since the original multidimensional maximum likelihood problem is decomposed into a sequence of much simpler one-dimensional problems of finding the peaks of notch periodograms. The ANPA achieves superresolution and a very low SNR threshold and can be computed and implemented in several efficient ways. First, with FFT and a concurrent Gram-Schmidt procedure using Schur's recursions, the notch periodogram can be computed without any costly eigendecomposition and matrix inversion. This approach can further lead to a mapping of the notch periodogram onto a VLSI architecture consisting mainly of a highly pipelined notch processor and two FFT processors. Second, without degrading the excellent performance of ANPA, the notch periodogram can be simplified and approximated to provide further computational reduction and implementational simplicity     

Second-order approximation of the autocorrelation matrix function

A second-order approximation to the autocorrelation matrix of a nonlinear transformation is presented and its use is illustrated on two examples. One example discusses the correction of the automatic gain control (AGC) effect in monopulse radar receivers.     

Rational approximation to transfer-function matrix of distributed system

A solution is given to the problem of finding a matrix of rational functions which is an approximation to the transfer-function matrix of a multivariable system described by a mixed set of partial and ordinary differential equations.     

Superresolution of multipath delay profiles measured by PNcorrelation method

Time resolution of multipath delay profiles measured by using the autocorrelation of a pseudonoise (PN) code sequence is generally limited by the chip interval of the PN code sequence. A superresolution PN correlation method (SPM) is proposed which improves the time resolution of delay profiles measured by the conventional PN correlation method. The SPM is based on a decomposition of the eigenvector space of the correlation matrix of the delay profile data vector and gives the number of paths and their delay times with higher resolution. It is verified by computer simulations and experiments using coaxial delay lines that the SPM can resolve two paths with a delay difference of a few tenths of the chip interval. The applicability of the SPM to the analysis of an indoor multipath environment in which many delayed waves arrive with short delay differences is demonstrated by an indoor radio propagation experiment at 2.3 GHz     

Superresolution of uncorrelated interference sources by using adaptive array techniques

By using adaptive techniques an antenna array can achieve an angular resolution of uncorrelated interference sources substantially greater than the aperture of diffraction limit. The antenna beam is scanned over the interference source locations, and for each scan condition the adaptive processor is allowed to reach its steady state. It is shown that for realistic ratios of interference strengths to system thermal noise, resolutions in excess of 0.25 times the Rayleigh limit can be achieved.     

Two methods for Toeplitz-plus-Hankel approximation to a datacovariance matrix

Recently, fast algorithms have been developed for computing the optimal linear least squares prediction filters for nonstationary random processes (fields) whose covariances have (block) Toeplitz-Hankel form. If the covariance of the random process (field) must be estimated from the data, the following problem is presented: given a data covariance matrix, computer from the available data, find the Toeplitz-plus-Hankel matrix closest to this matrix in some sense. The authors give two procedures for computing the Toeplitz-plus-Hankel matrix that minimizes the Hilbert-Schmidt norm of the difference between the two matrices. The first approach projects the data covariance matrix onto the subspace of Toeplitz-plus-Hankel matrices, for which basis functions can be computed using a Gram-Schmidt orthonormalization. The second approach projects onto the subspace of symmetric Toeplitz plus skew-persymmetric Hankel matrices, resulting in a much simpler algorithm. The extension to block Toeplitz-plus-Hankel data covariance matrix approximation is also addressed     

基于对角块分解的下行方向快速预编码算法

利用同一电缆包中布线的空间特殊性,提出一种抑制下行传输方向串音的预编码算法.一方面由于算法中仅涉及二阶矩阵的逆,运算量很小,易于实现.另一方面,此方法性能优于之前提出的一阶逼近算法,而与三对角线逼近算法性能相近,但运算量要小得多.基于实测数据的计算机仿真验证了结果的正确性.     

入射光场分布对超分辨光瞳滤波器超分辨性能和焦深的影响

光瞳滤波器是一种重要的调控焦点处光强分布的器件。借助光的标量衍射理论,研究了不同的入射光场分布对超分辨光瞳滤波器的超分辨性能和焦深的影响。研究结果表明:在入射总光能相同的情况下,光场以高斯函数分布入射时,与均匀光入射相比,其超分辨性能和焦深扩展特性变化很小。当光场以零阶贝塞尔函数分布入射时,光斑压缩比基本不变,斯特雷尔比有所下降,焦深有一定扩展。当光场以一阶贝塞尔函数分布入射时,光斑压缩比有所减小,斯特雷尔比有较大提高,焦深有所减小。总之,在相同情况下,光束的光强分布越靠近边缘,越有利于实现超分辨,斯特雷尔比和焦深两个量中其中一个的增大以另一个的减小为代价。     

Superresolution with second generation wavelets

Over the last 3 years or so, first-generation wavelets have been used to realize superresolution from a captured sequence of low-resolution (LR) degraded frames. Here, it is pointed out that second-generation wavelets (SGWs) are inherently more suited for image superresolution. From preliminary results that exploit subpixel displacements between LR frames to attain superresolution, it is concluded that SGWs show promise and potential to be extremely fast, efficient and versatile for superresolution.     

三维超分辨光瞳滤波器

提出一种改进的漏光型环形光瞳滤波器以期达到三维超分辨效果。对该光瞳滤波器与单透镜系统相结合的横向和轴向特性进行了详细分析 ,并给出了一个具有三维超分辨特性的光瞳实例。结果表明这种改进的漏光型光瞳滤波器具有三维超分辨能力 ,由于其轴向旁瓣强度太大 ,故利用共焦扫描成像系统点扩散函数乘积性抑制旁瓣 ,并取得较好的三维超分辨效果     

光学系统轴向超分辨滤波器的研究

运用最优化算法，存给定超分辨模型和爱里模型主瓣最大亮度比的斯特列耳比S的条件下，设计出3区振幅型轴向超分辨光瞳滤波器。给出设计模型和实例。结果表明，该超分辨滤波器优越于文献。     

一种超分辨距离多普勒成象方法

众所周知,距离多普勒成象雷达的距离分辨力和横向分辨力分别取决于发射信号的有效带宽和目标相对于雷达视线在相干处理区间内的转角,本文的研究工作旨在突破普通的FFT距离多普勒处理的限制,大大提高距离多普勒成象雷达的分辨能力,我们采用的方法是在进行付里叶重建之前用线性预测进行数据外推,用微波暗室试验数据进行转台成象的初步结果表明,这是一种改善距离多普勒成象雷达分辨能力的颇有前途的方法。     

Superresolution reconstruction using nonlinear gradient-based regularization

This paper discusses the problem of superresolution reconstruction. To preserve edges accurately and efficiently in the reconstruction, we propose a nonlinear gradient-based regularization that uses the gradient vector field of a preliminary high resolution image to configure a regularization matrix and compute the regularization parameters. Compared with other existing methods, it not only enhances the spatial resolution of the resulting images, but can also preserve edges and smooth noise to a greater extent. The advantages are shown in simulations and experiments with synthetic and real images.

Adaptive MIMO radar target parameter estimation with Kronecker-product structured interference covariance matrix

Multiple-Input Multiple-Output (MIMO) radar with colocated antennas has an increased target parameter estimation performance, but at the cost of increased computational complexity. This paper first presents the conditions required for the interference covariance matrix (ICM) of colocated MIMO radar to take a special structure, namely a Kronecker product of some sub-ICMs, and then proves that based on this ICM structure, the conventional Minimum Variance Distortionless Response (MVDR) algorithm can be reformulated into a combination of three estimation algorithms all of much smaller scales, such that the computational complexity is decreased significantly. However, this ICM structure can be destroyed by inactive scattering sources, whose influence is studied via numerical experiments. It is found that inactive point scatterers can still be suppressed by adaptive algorithms relying on the ICM structure, on condition that the number is fewer than that of receiving antennas.     

An efficient approach to multivariate Nakagami-m distribution using Green's matrix approximation

An efficient approach for the evaluation of the Nakagami-m (1960) multivariate probability density function (PDF) and cumulative distribution function (CDF) with arbitrary correlation is presented. Approximating the correlation matrix with a Green's matrix, useful closed formulas for the joint Nakagami-m PDF and CDF, are derived. The proposed approach is a significant theoretical tool that can be efficiently used in the performance analysis of wireless communications systems operating over correlative Nakagami-m fading channels.     

Efficient computation of DFT commuting matrices by a closed-form infinite order approximation to the second differentiation matrix

In order to define the discrete fractional Fourier transform, Hermite Gauss-like eigenvectors are needed and one way of extracting these eigenvectors is to employ DFT commuting matrices. Recently, Pei et al. exploited the idea of obtaining higher order DFT-commuting matrices, which was introduced by Candan previously. The upper bound of O(h^2k) approximation to N×N commuting matrix is 2k+1≤N in Candan's work and Pei et al. improved the proximity by removing this upper bound at the expense of higher computational cost. In this paper, we derive an exact closed form expression of infinite-order Taylor series approximation to discrete second derivative operator and employ it in the definition of excellent DFT commuting matrices. We show that in the limit this Taylor series expansion converges to a trigonometric function of second-order differentiating matrix. The commuting matrices possess eigenvectors that are closer to the samples of Hermite-Gaussian eigenfunctions of DFT better than any other methods in the literature with no additional computational cost.     

Angular Superresolution in Two-Dimensional Radar Problems

Journal of Communications Technology and Electronics - The inverse two-dimensional problem of forming a radio image of a signal source with angular superresolution has been solved. A new technique...     

Superresolution character of array confocal system

Theconfocalmicroscopysystem(CMS)withnon contact,highprecisionand3Ddetectingabilityplaysan importantroleinthe3Dmicrostructuremeasurement.Whiletheconventionalconfocalmicroscopycanonly scanthe3Dprofileinthewayofsinglepoint,itsspeedisnotenoughforfastmeasureme…     

多帧超分辨率重建中的图像插值

为了实现多帧超分辨率重建,必须从图像序列中提取子像素信息,因此要求图像的配准精确到子像素级。本文提出了一种超分辨率重建中运动矩阵的构造方法。为了提高矩阵的构造精度,该方法引入图像插值,用性能好但计算量较小的三次插值算子实现插值运算,并比较了三种常用插值核的性能。实验结果表明,选择适当的插值函数不仅不会明显增加计算量,而且可以显著提高矩阵的构造精度,从而大大提高多帧超分辨率重建图像的质量。