The state observer and compensator of a large class of 2-D acceptable singular systems

Under the assumption of nonexistence of the jump-mode, this paper gives a simple form of a large class of 2-D singular systems. This class of systems includes all the systems resulted from the linear state transformations of 2-D singular Roesser models and hence we called it the extended singular Roesser models. The criteria are presented for testing that via some suitable invertible linear state transformations, the given 2-D singular systems in the extended Roesser models can be converted equivalently to the classical Roesser models. Some results on 2-D classical singular Roesser model such as the reduced order regular observer and compensator design are generalized to the extended models.     

Two-dimensional frequency-domain blind system identification usinghigher order statistics with application to texture synthesis

In this paper, Shalvi and Weinstein's (1993) super-exponential (SE) algorithm using higher order statistics for blind deconvolution of one-dimensional (1-D) linear time-invariant systems is extended to a two-dimensional (2-D) SE algorithm. Then, a 2-D frequency-domain blind system identification (BSI) algorithm for 2-D linear shift-invariant (LSI) systems using the computationally efficient 2-D SE algorithm and the 2-D linear prediction error filter is proposed. In addition to the LSI system estimate, the proposed BSI algorithm also provides a minimum mean square error (MMSE) equalizer estimate and an MMSE signal enhancement filter estimate. Then, a texture synthesis method (TSM) using the proposed BSI algorithm is presented. Some simulation results to support the efficacy of the proposed BSI algorithm and some experimental results to support the efficacy of the proposed TSM are presented. Finally, some conclusions are drawn     

Design of two-dimensional nonrecursive filters based on frequencytransformations

Presents a simple and efficient method to design 2-D zero-phase nonrecursive filters based on frequency transformations. The method involves the formulation of an error along the desired contour in a quadratic form. It is shown that the method results in scaling-free transformation coefficients     

快速二维直方图斜分最小误差的图像阈值分割

鉴于二维斜分法的优势,提出了一种快速二维直方图斜分最小误差的阈值分割方法。首先将二维直方图斜分原理运用到最小误差阈值法中使得分割更准确,然后对其阈值选取公式进行简化得到最简公式,并利用此公式导出其一般递推算法,最后将二维直方图概率分布特性与这种算法有机结合得到新型的递推算法来提高运行速度。实验结果表明,与二维直线型最小误差阈值分割法相比,算法效率更高,与其递推算法相比,所提出的新型递推算法的运行速度更快,约快4倍。     

Adaptive Linear Predictive Coding of Time-Varying Images Using Multidimensional Recursive Least Squares Ladder Filters

This paper presents several adaptive linear predictive coding techniques based upon extension of recursive ladder filters to two and three dimensions (2-D/3-D). A 2-D quarter-plane autoregressive ladder filter is developed using a least square criterion in an exact recursive fashion. The 2-D recursive ladder filter is extended to a 3-D case which can adaptively track the variation of both spatial and temporal changes of moving images. Using the 2-D/3-D ladder filters and a previous frame predictor, two types of adaptive predictor-control schemes are proposed in which the prediction error at each pel can be obtained at or close to a minimum level. We also investigate several modifications of the basic encoding methods. Performance of the 2D/3-D ladder filters, their adaptive control schemes, and variations in coding methods are evaluated by computer simulations on two real sequences and compared to the results of motion compensation and frame differential coders. As a validity test of the ladder filters developed, the error signals for the different predictors are compared and the visual quality of output images is verified.     

Design of two-dimensional digital filters via spectral transformations

Complex maps, with domains and codomains consisting of rational transfer functions, have often been used in designing two-dimensional (2-D) digital filters. Such maps, commonly known as spectral transformations, have the important property of carrying a stable rational transfer function to another stable rational function. This paper presents a unified framework for designing 2-D stable digital filters from prescribed magnitude-response specifications using spectral transformations such that the magnitude response of the resultant approximation is sort of a "best" approximation of the given specification. It is shown that there are two basic strategies for such designs, each with its own advantages and disadvantages. The design procedures are illustrated with practical examples. Further, it is also shown that all earlier results on 2-D filter design using spectral transformations follow as special cases of the general theory presented here.     

Two-dimensional Fourier series-based model for nonminimum-phaselinear shift-invariant systems and texture image classification

In this paper, Chi's (1997, 1999) real one-dimensional (1-D) parametric nonminimum-phase Fourier series-based model (FSBM) is extended to two-dimensional (2-D) FSBM for a 2-D nonminimum-phase linear shift-invariant system by using finite 2-D Fourier series approximations to its amplitude response and phase response, respectively. The proposed 2-D FSBM is guaranteed stable, and its complex cepstrum can be obtained from its amplitude and phase parameters through a closed-form formula without involving complicated 2-D phase unwrapping and polynomial rooting. A consistent estimator is proposed for the amplitude estimation of the 2-D FSBM using a 2-D half plane causal minimum-phase linear prediction error filter (modeled by a 2-D minimum-phase FSBM), and then, two consistent estimators are proposed for the phase estimation of the 2-D FSBM using the Chien et al. (1997) 2-D phase equalizer (modeled by a 2-D all-pass FSBM). The estimated 2-D FSBM can be applied to modeling of 2-D non-Gaussian random signals and 2-D signal classification using complex cepstra. Some simulation results are presented to support the efficacy of the three proposed estimators. Furthermore, classification of texture images (2-D non-Gaussian signals) using the estimated FSBM, second-, and higher order statistics is presented together with some experimental results. Finally, we draw some conclusions     

Wavelet packets for fast solution of electromagnetic integralequations

This paper considers the problem of wavelet sparsification of matrices arising in the numerical solution of electromagnetic integral equations by the method of moments. Scattering of plane waves from two-dimensional (2-D) cylinders is computed numerically using a constant number of test functions per wavelength. Discrete wavelet packet (DWP) similarity transformations and thresholding are applied to system matrices to obtain sparsity. If thresholds are selected to keep the relative residual error constant the matrix sparsity is of order O(N^P) with p<2. This stands in contrast with O(N² ) sparsities obtained with standard wavelet transformations. Numerical tests also show that the DWP method yields faster matrix-vector multiplication than some fast multipole algorithms     

Maximum-likelihood parameter estimation of discrete homogeneousrandom fields with mixed spectral distributions

This paper presents a maximum-likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued, 2-D, homogeneous random field with mixed spectral distribution. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanescent. The proposed algorithm provides a complete solution to the joint estimation problem of the random field components. By introducing appropriate parameter transformations, the highly nonlinear least-squares problem that results from the maximization of the likelihood function is transformed into a separable least-squares problem. In this new problem, the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares. Solution of the transformation equations provides a complete solution of the field model parameter estimation problem     

Consistent landmark and intensity-based image registration

Two new consistent image registration algorithms are presented: one is based on matching corresponding landmarks and the other is based on matching both landmark and intensity information. The consistent landmark and intensity registration algorithm produces good correspondences between images near landmark locations by matching corresponding landmarks and away from landmark locations by matching the image intensities. In contrast to similar unidirectional algorithms, these new consistent algorithms jointly estimate the forward and reverse transformation between two images while minimizing the inverse consistency error-the error between the forward (reverse) transformation and the inverse of the the reverse (forward) transformation. This reduces the ambiguous correspondence between the forward and reverse transformations associated with large inverse consistency errors. In both algorithms a thin-plate spline (TPS) model is used to regularize the estimated transformations. Two-dimensional (2-D) examples are presented that show the inverse consistency error produced by the traditional unidirectional landmark TPS algorithm can be relatively large and that this error is minimized using the consistent landmark algorithm. Results using 2-D magnetic resonance imaging data are presented that demonstrate that using landmark and intensity information together produce better correspondence between medical images than using either landmarks or intensity information alone.     

A linear systolic array for recursive least squares

Classical systolic design procedures rely on linear or affine space-time transformations because of the well-understood properties of linear operations. In order to increase the efficiency of the final processor, various ad hoc manipulations applied to transformations that appeared to be nonlinear at the physical array level have been proposed. Folding is one of these possible transformations. The authors show that folding can actually be considered to be an overall linear procedure by artificially increasing the dimensionality of the dependence graph of the algorithm. A 1-D array for recursive least squares is also derived as an application of a systematic linear design procedure including folding     

基于先验相位结构信息的双基SAR两维自聚焦算法

两维自聚焦是高机动条件下机载合成孔径雷达(SAR)高分辨率成像的重要保障。现有的双基SAR两维自聚焦算法没有充分利用相位误差的先验结构信息,是对相位误差的一种盲估计,在计算效率和参数估计精度方面仍然存在很大限制。该文从双基SAR极坐标格式成像算法新解释入手,从残留距离徙动(RCM)校正的观点出发,将极坐标格式(PFA)算法的实现解释为距离频率和方位时间两个变量的解耦过程。利用这一观点分析了极坐标格式算法中的距离和方位重采样对两维相位误差的影响,揭示了残留两维相位误差固有的解析结构。基于这一固有的先验信息,该文提出了一种结合先验信息和图像数据的双基SAR两维自聚焦算法。算法通过引入先验知识,将两维相位误差估计降维成一维方位相位误差的估计;同时,在估计方位相位误差时,通过多子带数据平均,充分挖掘了所有数据的信息。相比于已有算法,无论是参数估计精度还是计算效率都有明显改善。实验结果验证了该文理论分析的正确性以及所提两维自聚焦方法的有效性。      

FDTD-Modelling of Dispersive Nonlinear Ring Resonators: Accuracy Studies and Experiments

The accuracy of nonlinear finite-difference time-domain (FDTD) methods is investigated by modeling nonlinear optical interaction in a ring resonator. We have developed a parallelized 3-D FDTD algorithm which incorporates material dispersion, chi⁽³⁾-nonlinearities and stair-casing error correction. The results of this implementation are compared with experiments, and intrinsic errors of the FDTD algorithm are separated from geometrical uncertainties arising from the fabrication tolerances of the device. A series of progressively less complex FDTD models is investigated, omitting material dispersion, abandoning the stair-casing error correction, and approximating the structure by a 2-D effective index model. We compare the results of the different algorithms and give guidelines as to which degree of complexity is needed in order to obtain reliable simulation results in the linear and the nonlinear regime. In both cases, incorporating stair-casing error correction and material dispersion into a 2-D effective index model turns out to be computationally much cheaper and more effective than performing a fully three-dimensional simulation without these features     

结构光三维视觉检测系统的标定方法研究

提出了一种新的结构光三维视觉检测系统的标定方法,将BP神经网络和线性标定方法结合起来,用线性标定方法标定结构光系统的线性部分,用BP神经网络来描述该结构光系统的其他部分.结果表明:该方法结合了神经网络和线性标定方法的优点,不仅给出了结构光三维检测系统中CCD相机的内部和外部参数,而且利用神经网络的非线性逼近能力,补偿由于镜头径向畸变、切向畸变等因素引起的系统非线性误差,并且精度高、抗噪声能力强及鲁棒性好.     

On the properties of linear spectral transformations for 2-dimensional digital filters

A set of eight linear spectral transformations which can be used in the design of two-dimensional digital filters is studied from a group-theoretic point of view. Several properties of the transformations, some of them known and some of them new, are deduced and are then applied in the implementation of 2-D digital filters. It is shown that trade-offs exist which can be used to reduce either the amount of memory required for the programming or the amount of data manipulation.     

一类冗余比为2的二维DFT调制滤波器组的设计

本文构建了一类冗余比为2的二维线性相位的双原型离散傅立叶变换（DFT）调制滤波器组。利用原型滤波器的多相位分解,推导出了该滤波器组的完全重构(PR)条件。基于该PR条件,我们将滤波器组的设计归结为一个关于原型滤波器的多相位分量的无约束优化问题。由于原型滤波器是线性相位的,多相位分量之间具有一定的关系,因此我们可以简化该优化问题。仿真结果验证了滤波器组PR条件的正确性。同时,仿真表明了优化算法的有效性,设计所得的滤波器组重构误差很小、频率特性较好,基本满足实际应用的需要。      

Parametric cumulant based phase estimation of 1-D and 2-Dnonminimum phase systems by allpass filtering

This paper proposes a parametric cumulant-based phase-estimation method for one-dimensional (1-D) and two-dimensional (2-D) linear time-invariant (LTI) systems with only non-Gaussian measurements corrupted by additive Gaussian noise. The given measurements are processed by an optimum allpass filter such that a single Mth-order (M⩾3) cumulant of the allpass filter output is maximum in absolute value. It can be shown that the phase of the unknown system of interest is equal to the negative of the phase of the optimum allpass filter except for a linear phase term (a time delay). For the phase estimation of 1-D LTI systems, an iterative 1-D algorithm is proposed to find the optimum allpass filter modeled either by an autoregressive moving average (ARMA) model or by a Fourier series-based model. For the phase estimation of 2-D LTI systems, an iterative 2-D algorithm is proposed that only uses the Fourier series-based allpass model. A performance analysis is then presented for the proposed cumulant-based 1-D and 2-D phase estimation algorithms followed by some simulation results and experimental results with real speech data to justify their efficacy and the analytic results on their performance. Finally, the paper concludes with a discussion and some conclusions     

Two-dimensional retiming [VLSI design]

This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques     

Consistent image registration

This paper presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another. This approach produces a consistent set of transformations that have less pairwise registration error, i.e., better correspondence, than traditional methods that estimate the forward and reverse transformations independently. The transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics. The transformations are parameterized by a Fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation. Results using a linear elastic material constraint are presented using both magnetic resonance and X-ray computed tomography image data. The results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity give better registration results than using either constraint alone or none at all.