Canonical coordinates for transform coding of noisy sources

Based on the additive white quantization noise model, linear transform coders are derived for Gaussian sources corrupted by noise. There are two alternative design objectives: minimizing the trace of the error correlation matrix and thus minimizing the mean-squared error, or minimizing the determinant of the error correlation matrix and thus maximizing information rate. It is shown that a solution to both problems is to first transform the noisy observations into canonical coordinates, quantize and apply a Wiener filter in this coordinate system, and then transform the result back to the original coordinates. Canonical coordinates are uncorrelated, and quantization and Wiener filtering are applied to each component independently. The type of canonical coordinate system depends on the design objective: Quantization in half-canonical coordinates minimizes the mean-squared error and quantization in full-canonical coordinates maximizes information rate. Finally, it is also demonstrated in this paper that majorization is the fundamental principle underlying proofs of optimal transform coding.     

基于小波变换的图像Wiener滤波并行实现

面向大规模数据图像去噪处理高效实现,本文提出一种基于Daubechies 9—7小波分解的方向窗Wiener滤波并行实现方法和阵列结构。首先针对小波变换给出了提升小波变换的并行实现方法和PE间的互联结构。该实现方法极大地加速了小波变换的速度,同时其互联结构又确保了各变换层中存放相同子带系数的PE的直接互联,有效地减少了小波变换和去噪处理中的通信开销。针对Wiener滤波中各子带滑动窗累加求和问题,采用循环前缀求和的处理方式,并行地实现了多窗口的累加求和,极大地降低了Wiener滤波的时间开销,满足大图像帧处理的实时性要求。     

Split Wiener filtering with application in adaptive systems

This paper proposes a new structure for split transversal filtering and introduces the optimum split Wiener filter. The approach consists of combining the idea of split filtering with a linearly constrained optimization scheme. Furthermore, a continued split procedure, which leads to a multisplit filter structure, is considered. It is shown that the multisplit transform is not an input whitening transformation. Instead, it increases the diagonalization factor of the input signal correlation matrix without affecting its eigenvalue spread. A power normalized, time-varying step-size least mean square (LMS) algorithm, which exploits the nature of the transformed input correlation matrix, is proposed for updating the adaptive filter coefficients. The multisplit approach is extended to linear-phase adaptive filtering and linear prediction. The optimum symmetric and antisymmetric linear-phase Wiener filters are presented. Simulation results enable us to evaluate the performance of the multisplit LMS algorithm.     

A summary, by illustrations, of least-squares filters with constraints

Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least-squares criterion is used to design the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various constraints on the filter coefficients rather than being given as a signal correlation function. The equations are worked out explicitly for the case of two time series and three filter points and presented in such a way as to make generalization clear.     

Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication

This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L²(R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual twochannel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel     

Eigenfilter Approach to the Design of One-Dimensional and Multidimensional Two-Channel Linear-Phase FIR Perfect Reconstruction Filter Banks

We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a “predesigned” analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.      

Wiener filters in canonical coordinates for transform coding,filtering, and quantizing

Canonical correlations are used to decompose the Wiener filter into a whitening transform coder, a canonical filter, and a coloring transform decoder. The outputs of the whitening transform coder are called canonical coordinates; these are the coordinates that are reduced in rank and quantized in our finite-precision version of the Gauss-Markov theorem. Canonical correlations are, in fact, cosines of the canonical, angles between a source vector and a measurement vector. They produce new formulas for error covariance, spectral flatness, and entropy     

Transmit patterns for active linear arrays with peak amplitude andradiated voltage distribution constraints

Distribution functions used in array antenna design typically synthesize specified pattern characteristics without consideration for either the peak amplitude of the radiating elements or the aperture radiated power. There do exist applications, however, in which the pattern synthesis must employ such constraints. In the transmit mode of active array antennas, for example, it is desirable to radiate as much power as possible subject to a per-element peak amplitude constraint while simultaneously suppressing the outer sidelobes. This paper discusses the design considerations of the constrained least squares (CLS) distribution function. In the CLS distribution, most of the radiating elements near the array center are set to their maximum value while only a few of the outer elements are tapered. A method for generating CLS distributions given constraints on both the peak element amplitude and the total effective radiated voltage (ERV) is discussed. The design involves specifying the desired ERV and a weighting function that allows selectively suppressing sidelobes in specified regions. The effects of these design parameters on the far-field patterns are explored     

一种基于三正交约束的摄像机标定方法

提出一种基于三正交约束的摄像机标定方法.设定摄像机坐标系为世界坐标系,标定摄像机内参数中的5个未知量和1个投影缩放因子,设计一种由7个空间点组成的标定模板,在不需要已知标定模板线段长度的情况下,仅需要2幅以上不同姿态标定模板的图像即可根据三正交关系建立约束方程组,通过矩阵特征值分解,求得摄像机内参数的解析解.对同一个摄像机进行对比实验,本文标定结果与平面经典法标定结果的相对误差仅为1.3%左右,且仿真数据实验和真实图像实验的结果表明,该算法具有较高的标定精度和鲁棒性.     

基于维纳滤波语音增强算法的改进实现

通过对维纳滤波的介绍,实现了基本维纳滤波效果;利用两级维纳滤波和两级滤波器组滤波方法实现了语音增强,达到了良好的效果.     

无人机交替中继通信及其轨迹优化和功率分配研究

为了提高无人机中继通信系统的频谱利用率,该文提出一种交替中继方法,通过两个无人机中继交替工作,轮流将信息从源端转发到目的端。研究联合优化无人机中继的飞行轨迹和各发射端的发射功率,协调两条中继链路的相互干扰,实现端到端的吞吐量最大化。涉及的优化问题受限于无人机的高度约束、机动约束、防碰撞约束以及各发射端的平均与峰值发射功率约束,是难以求得最优解的非凸优化问题。该文提出一种基于交替最大化和连续凸优化技术的高效迭代算法求解次优解,并用计算机仿真验证了所提算法的有效性。     

Minimax design of two-channel nonuniform-division FIR filter banks

The paper deals with the minimax design of two-channel nonuniform-division filter (NDF) banks. Based on a linearisation scheme, the design problem is formulated as an optimisation problem with linear constraints. The authors present a method to design a two-channel NDF bank using a modified dual-affine scaling variant of Karmarkar's (1984) algorithm. This method provides the optimal results that the linear-phase FIR analysis and synthesis filters have equiripple stopband response and the resulting NDF bank also shows equiripple reconstruction error behaviour. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)

In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.     

Motion-compensating prediction with fractional-pel accuracy

The effect of fractional-pel accuracy on the efficiency of motion-compensating predictors is studied using various spatial prediction/interpolation filters. In model calculations, the power spectral density of the prediction error is related to the probability density function of the displacement error. Prediction can be improved both by higher accuracy of motion-compensation and by spatial Wiener filtering in the predictor. Beyond a critical accuracy, the possibility of further improving prediction by more accurate motion-compensation is small. Experiments with videophone signals and with broadcast TV signals confirm these model calculations. Sinc-interpolation, bilinear interpolation, and Wiener filtering are compared at integer-pel, 1/2-pel, 1/4-pel, and 1/8-pel accuracies. A three-state technique for reliable displacement estimation with fractional-pel accuracy is introduced. It is based on phase correlation. For motion-compensation with block size of 16 pels×16 pels, 1/4-pel accuracy appears to be sufficient for broadcast TV signals, whereas for videophone signals, 1/2-pel accuracy is desirable     

On three-dimensional rotations, coordinate frames, and canonicalforms for it all

Some properties of the eigenproblem for a three-dimensional rotation matrix are shown, and related to the geometrical rotation parameters. The problem of assigning a unique canonical coordinate frame to a set of three mutually orthogonal axes is considered. The assignment is such that it corresponds to a minimal overall rotation with respect to the reference system. It is noted that this problem is of interest for the unique and consistent labeling of the principal axes of various tensors related to physical properties of materials, and symmetric matrices that appear in various disciplines of engineering     

Interconversion between truncated Cartesian and polar expansions of images.

In this paper, we propose an algorithm for lossless conversion of data between Cartesian and polar coordinates, when the data is sampled from a 2-D real-valued function (a mapping: R2 --> R) expressed as a particular kind of truncated expansion. We use Laguerre functions and the Fourier basis for the polar coordinate expression. Hermite functions are used for the Cartesian coordinate expression. A finite number of coefficients for the truncated expansion specifies the function in each coordinate system. We derive the relationship between the coefficients for the two coordinate systems. Based on this relationship, we propose an algorithm for lossless conversion between the two coordinate systems. Resampling can be used to evaluate a truncated expansion on the complementary coordinate system without computing a new set of coefficients. The resampled data is used to compute the new set of coefficients to avoid the numerical instability associated with direct conversion of the coefficients. In order to apply our algorithm to discrete image data, we propose a method to optimally fit a truncated expression to a given image. We also quantify the error that this filtering process can produce. Finally the algorithm is applied to solve the polar-Cartesian interpolation problem.     

New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al (1995). The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods.     

Minimax estimation of unknown deterministic signals in colorednoise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem     

An overview of morphological filtering

This paper consists of a tutorial overview of morphological filtering, a theory introduced in 1988 in the context of mathematical morphology. Its first section is devoted to the presentation of the lattice framework. Emphasis is put on the lattices of numerical functions in digital and continuous spaces. The basic filters, namely the openings and the closings, are then described and their various versions are listed. In the third section morphological filters are defined as increasing idempotent operators, and their laws of composition are proved. The last sections are concerned with two special classes of filters and their derivations: first, the alternating sequential filters allow us to bring into play families of operators depending on a positive scale parameter. Finally, the center and the toggle mappings modify the function under study by comparing it, at each point, with a few reference transforms.     

基于多级维纳滤波的低秩盲空时多用户检测

应用最大最小原理实现了广义正则形式的最小方差空时多用户检测,并采用多级维纳滤波结构提出了一种新的低秩处理算法。进一步与现有的几种低秩处理算法进行了比较,分析了秩的选择对系统性能的影响。