Two-dimensional orthogonal lattice structures for autoregressivemodeling of random fields

Two-dimensional orthogonal lattice filters are developed as a natural extension of the 1-D lattice parameter theory. The method offers a complete solution for the Levinson-type algorithm to compute the prediction error filter coefficients using lattice parameters from the given 2-D augmented normal equations. The proposed theory can be used for the quarter-plane and asymmetric half-plane models. Depending on the indexing scheme in the prediction region, it is shown that the final order backward prediction error may correspond to different quarter-plane models. In addition to developing the basic theory, the article includes several properties of this lattice model. Conditions for lattice model stability and an efficient method for factoring the 2-D correlation matrix are given. It is shown that the unended forward and backward prediction errors form orthogonal bases. A simple procedure for reduced complexity 2-D orthogonal lattice filters is presented. The proposed 2-D lattice method is compared with other alternative structures both in terms of conceptual background and complexity. Examples are considered for the given covariance case     

基于三维自适应预测的高光谱图像无损压缩算法

利用高光谱图像具有较强的谱间相关性的特点,本文提出一种基于三维自适应预测的高光谱图像无损压缩方法,首先根据相关系数计算波段预测顺序,然后利用相关性较强的空间邻点和谱间邻点,采用基于神经网络模型的自适应预测方法进行三维预测编码.实验结果表明,该方法能够有效的去除高光谱图像的空间和谱间相关性,与现在最优的无损压缩国际标准JPEG-LS相比,压缩后的平均比特率能够降低0.3bpp左右.     

Computationally efficient two-dimensional Capon spectrum analysis

We present a computationally efficient algorithm for computing the 2-D Capon (1969) spectral estimator. The implementation is based on the fact that the 2-D data covariance matrix will have a Toeplitz-block-Toeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg-Heinig (1974) formula that is a function of strictly the forward 2-D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the difference in the so-obtained 2-D spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the Whittle-Wiggins-Robinson (1963, 1965) algorithm. Numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well-known classical implementation and the method published by Liu et al.(see IEEE Trans. Aerosp. Electron. Syst., vol.34, p.1314-19, 1998)     

Further improved 2-D lattice filter structure employing missing reflection coefficients

A new lattice filter structure to model two-dimensional (2-D) autoregressive (AR) fields is proposed. The proposed structure utilizes and extracts the information contained in the backward prediction error fields and their delayed versions. The main idea is to use two sets of reflection coefficients corresponding to two quadrant filters and to increase the number of reflection coefficients with the order of the lattice filter. Increasing the number of reflection coefficients at each stage produces a sufficient number of independent parameters to model AR fields up to order three, which is an improvement over the existing 2-D lattice filter structures. The improvement is confirmed by computer simulations. In addition, a relationship between the reflection coefficients and the AR coefficients is derived. It is also shown that the entropy contained in the backward prediction error field vector of the proposed structure is closer to the input entropy when compared to those contained in existing 2-D lattice filters.     

Multispectral code excited linear prediction coding and itsapplication in magnetic resonance images

This paper reports a multispectral code excited linear prediction (MCELP) method for the compression of multispectral images. Different linear prediction models and adaptation schemes have been compared. The method that uses a forward adaptive autoregressive (AR) model has been proven to achieve a good compromise between performance, complexity, and robustness. This approach is referred to as the MFCELP method. Given a set of multispectral images, the linear predictive coefficients are updated over nonoverlapping three-dimensional (3-D) macroblocks. Each macroblock is further divided into several 3-D micro-blocks, and the best excitation signal for each microblock is determined through an analysis-by-synthesis procedure. The MFCELP method has been applied to multispectral magnetic resonance (MR) images. To satisfy the high quality requirement for medical images, the error between the original image set and the synthesized one is further specified using a vector quantizer. This method has been applied to images from 26 clinical MR neuro studies (20 slices/study, three spectral bands/slice, 256x256 pixels/band, 12 b/pixel). The MFCELP method provides a significant visual improvement over the discrete cosine transform (DCT) based Joint Photographers Expert Group (JPEG) method, the wavelet transform based embedded zero-tree wavelet (EZW) coding method, and the vector tree (VT) coding method, as well as the multispectral segmented autoregressive moving average (MSARMA) method we developed previously.     

A fundamental theorem of algebra, spectral factorization, and stability of two-dimensional systems

In his doctoral dissertation in 1797, Gauss proved the fundamental theorem of algebra, which states that any one-dimensional (1-D) polynomial of degree n with complex coefficients can be factored into a product of n polynomials of degree 1. Since then, it has been an open problem to factorize a two-dimensional (2-D) polynomial into a product of basic polynomials. Particularly for the last three decades, this problem has become more important in a wide range of signal and image processing such as 2-D filter design and 2-D wavelet analysis. In this paper, a fundamental theorem of algebra for 2-D polynomials is presented. In applications such as 2-D signal and image processing, it is often necessary to find a 2-D spectral factor from a given 2-D autocorrelation function. In this paper, a 2-D spectral factorization method is presented through cepstral analysis. In addition, some algorithms are proposed to factorize a 2-D spectral factor finely. These are applied to deriving stability criteria of 2-D filters and nonseparable 2-D wavelets and to solving partial difference equations and partial differential equations.     

MULTI-SPECTRAL AND HYPERSPECTRAL IMAGE FUSION USING 3-D WAVELET TRANSFORM

Image fusion is performed between one band of multi-spectral image and two bands of hyperspectral image to produce fused image with the same spatial resolution as source multi-spectral image and the same spectral resolution as source hyperspeetral image. According to the characteristics and 3-Dimensional （3-D） feature analysis of multi-spectral and hyperspectral image data volume, the new fusion approach using 3-D wavelet based method is proposed. This approach is composed of four major procedures： Spatial and spectral resampling, 3-D wavelet transform, wavelet coefficient integration and 3-D inverse wavelet transform. Especially, a novel method, Ratio Image Based Spectral Resampling （RIBSR）method, is proposed to accomplish data resampling in spectral domain by utilizing the property of ratio image. And a new fusion rule, Average and Substitution （A＆S） rule, is employed as the fusion rule to accomplish wavelet coefficient integration. Experimental results illustrate that the fusion approach using 3-D wavelet transform can utilize both spatial and spectral characteristics of source images more adequately and produce fused image with higher quality and fewer artifacts than fusion approach using 2-D wavelet transform. It is also revealed that RIBSR method is capable of interpolating the missing data more effectively and correctly, and A＆S rule can integrate coefficients of source images in 3-D wavelet domain to preserve both spatial and spectral features of source images more properly.     

Fine estimators of two-dimensional parameters and application tospatial shift estimation

This paper presents a fast technique for fine estimation of two-dimensional (2-D) parameters, based on a parabolic interpolation of the same ambiguity function samples, and aimed at block-oriented estimation of the spatial shift between pairs of images in video sequences. Expressions for the bias and variance of the position error and the prediction error are derived. The method is tested using a synthetically generated autocorrelation function, varying the directionality and the eccentricity factor, in order to compare the performance of the proposed 2-D estimator to the case of two separate one-dimensional (1-D) estimators. The method has also been applied in vision systems, evidencing encouraging results for estimating the parameters of sophisticated global motion models from real images     

Wavelet-based hybrid ECG compression technique

In this paper, a new wavelet-based hybrid electrocardiogram (ECG) data compression technique is proposed. Firstly, in order to fully utilize the two correlations of heartbeat signals, 1-D ECG data are segmented and aligned to a 2-D data arrays. Secondly, 2-D wavelet transform is applied to the constructed 2-D data array. Thirdly, the set partitioning hierarchical trees (SPIHT) method and the vector quantization (VQ) method are modified, according to the individual characteristic of different coefficient subband and the similarity between the subbands. Finally, a hybrid compression method of the modified SPIHT and VQ is employed to the wavelet coefficients. Records selected from the MIT/BIH arrhythmia database are tested. The experimental results show that the proposed method is suitable for various morphologies of ECG data, and that it achieves high compression ratio with the characteristic features well preserved.     

Design Of 2-D Recursive Digital Filters Using Nonsymmetric Half-Plane Allpass Filters

A novel structure using recursive nonsymmetric half-plane (NSHP) digital allpass filters (DAFs) is presented for designing 2-D recursive digital filters. First, several important properties of 2-D recursive DAFs with NSHP support regions for filter coefficients are investigated. The stability of the 2-D recursive NSHP DAFs is guaranteed by using a spectral factorization-based algorithm. Then, the important characteristics regarding the proposed novel structure are discussed. The design problem of 2-D recursive digital filters using the novel structure is considered. We formulate the problem by forming an objective function consisting of the weighted sum of magnitude, group delay, and stability-related errors. A design technique using a trust-region Newton-conjugate gradient method in conjunction with the analytic derivatives of the objective function is presented to efficiently solve the resulting optimization problem. The novelty of the presented 2-D structure is that it possesses the advantage of better performance in designing a variety of 2-D recursive digital filters over existing 2-D filter structures. Finally, several design examples are provided for conducting illustration and comparison.     

High resolution two-dimensional minimum free energy AR spectral estimation

We extend the minimum free energy (MFE) parameter estimation method to 2-D fields. This 2-D MFE method may be used to determine autoregressive (AR) model parameters for spectral estimation of 2-D fields. It may also be used to provide AR models for texture synthesis. The performance of the technique for closely spaced sinusoids in white noise is demonstrated by numerical example. Better results can be achieved than with the multidimensional Levinson algorithm.     

A new texture generation method based on pseudo-DCT coefficients.

In this paper, a new method for generating different texture images is presented. This method involves a simple transform from a certain one-dimensional (1-D) signal to an expected two-dimensional (2-D) image. Unlike traditional methods, the input signal is generated by a simple 1-D function in our work instead of a sample texture. We first transform the 1-D input signal into frequency domain using fast Fourier transform. Based on the sufficient analysis in 2-D discrete cosine transform (DCT) domain, where each of the coefficients expresses a texture feature in a certain direction, the 2-D pseudo-DCT coefficients are then constructed by appropriately rearranging the Fourier coefficients in terms of their frequency components. Finally, the corresponding texture image can be produced by 2-D inverse DCT algorithm. We applied the proposed method to generate several stochastic textures (i.e., cloud, illumination, and sand), and several structural texture images. Experimental results indicate the good performance of the proposed method.     

On the Parameter Estimation of 2-D Moving Average Random Fields

The problem of estimating the parameters of 2-D homogeneous moving average (MA) random fields only from output measurements is addressed. A novel computationally efficient algorithm for the estimation of the parameters of a minimum-phase 2-D MA model with a nonsymmetric half-plane (NSHP) region of support (ROS) is proposed. Using the 2-D spectral factorization, relationship between the NSHP MA model parameters and the cepstral coefficients of a 2-D MA random field is considered. Based on this relation, recursive equations are derived so as to estimate the NSHP MA model parameters. It is noteworthy that the proposed algorithm is practical, i.e., it does not require computationally complex processes namely fitting to a high-order autoregressive model, any initial estimates, nor matrix inversion. Performance analysis of the derived algorithm together with an existing method is given for comparison purposes. Index     

基于小波变换与支持向量机回归的冬小麦叶面积指数估算

叶面积指数(LAI)是作物长势诊断及产量预测的重要参数。通过对冬小麦采样点的高光谱曲线进行连续小波变换(CWT),然后利用小波系数与LAI 建立支持向量机回归(SVR)模型,实现冬小麦不同生育时期的叶面积指数估算。通过对所研究方法与选取的植被指数、偏最小二乘(PLS)回归等5种方法的反演结果进行统计分析。结果表明:利用连续小波变换确定的LAI 的敏感波段为680、739、802、895 nm,对应尺度分别为8、4、9 和8,对应小波系数的LAI 回归确定系数(R2)明显高于冠层反射率的回归确定系数;利用小波系数与LAI 建立的SVR 模型的反演精度最高,模型实测值与预测值的检验精度(R2)为0.86,均方根误差(RMSE)为0.43;而常用植被指数(归一化植被指数,NDVI;比值植被指数,RVI)建立的估测模型对冬小麦多个生育时期LAI 反演精度最低(R2 0.76,RMSE0.56)。因此利用连续小波变换进行数据预处理,能更好地筛选出对叶面积指数敏感的信息,LAI 回归方法比较结果表明,SVR 比PLS 更适合于LAI 的估测,通过将CWT 与SVR 结合(CWT-SVR)能实现不同生育时期冬小麦叶面积指数的遥感估算。     

一种用于预测蚕丝含量占比的近红外光谱分析方法

针对近红外光谱分析技术中未充分利用预测模型光谱数据的问题,提出了一种可充分利用光谱数据和有效预测蚕丝含量占比的新方法。以5种类型共145个样本的蚕丝含量占比以及相应的所有蛋白质基光谱数据为研究对象,将这些样本分别划分为校正集和验证集,并采用偏最小二乘回归(Partial Least Squares Regression,PLSR)方法和提出的偏最小二乘回归多模型(multi--model Partial Least Squares Regression,multi--PLSR)方法建立了预测模型。然后对比和观察了两种方法的预测效果。以类型2的蚕丝样本为例,选用13个主成分并对比两种模型后发现,multi--PLSR模型的相关系数由0.594增至0.9784,平均相对误差由0.4866降至0.1384。实验结果表明,新方法充分利用了光谱数据中的信息,提高了蚕丝含量占比预测模型的精度,为建立近红外光谱预测模型提供了一种新思路。     

Optimum quarter-plane autoregressive modeling of 2-D fields usingfour-field lattice approach

A new orthogonal four-field two-dimensional (2-D) quarter-plane lattice structure with a complete set of reflection coefficients is developed by employing appropriately defined auxiliary prediction errors. This work is the generalization of the three-parameter lattice filter proposed by Parker and Kayran (1984). After the first stage, four auxiliary forward and four auxiliary backward prediction errors are generated in order to obtain a growing number of 2-D reflection coefficients at successive stages. The theory has been proven by using a geometrical formulation based on the mathematical concepts of vector space, orthogonal projection, and subspace decomposition. It is shown that all four quarter-plane filters are orthogonal and thus optimum for all stages. In addition to developing the basic theory, a set of orthogonal backward prediction error fields for successive lattice parameter model stages is presented     

基于改进的K-L变换的多光谱图像压缩算法

融合离散小波变换(DWT,discrete wavelet tran sform)与Karhunen-Loeve变换(KLT),将图像的能量集中到少数系数上,以达到更好的 压缩效果。首先将多光谱图像的每个谱段进行快速9/72D DWT,消除多光谱图像的大部分 空间冗余;然后对所有谱段产生的小波系数进行改进的KLT,来消除光谱冗余和残存的空 间冗余;最后对所得谱段产生的小波系数进行改进的KLT,来消除光谱冗余和残存的空间冗 余;最后对所得系数进行熵编码,得到压缩码流。实验结果表明,在码率为0.25～2.0bit/ pixel范围内,平均信噪比(SNR)高于41dB,同时缩短了运 算时间,从而提升了多光谱图像压 缩算法的性能。     

导数同步荧光光谱结合遗传优化算法测定鸭蛋蛋清中庆大霉素含量

为实现鸭蛋蛋清中庆大霉素(GM)残留含量的快速测定与检测模型精度的提高,应用遗传算法(GA)筛选导数同步荧光光谱特征波长,用遗传-支持向量回归(GA-SVR)建立鸭蛋蛋清中GM残留含量的预测模型。首先分析了样本的三维同步荧光光谱和确定了本实验研究的波长差Δλ为120nm;然后利用sym5小波的2层分解对一阶导数同步荧光光谱进行去噪处理,并利用GA筛选出了14个荧光特征波长;最后利用GA优化了SVR的径向基核函数(RBF)参数(c,g,p),进而比较了GA-SVR、PLS和MLR 3种预测模型的预测能力,研究表明,以GA-SVR模型的预测能力最强,其预测集的决定系数(R2)和均方根误差(RMSEP)分别为0.983 0和1.149 4mg/L。实验结果表明,GA能有效筛选出鸭蛋蛋清中GM的荧光特征波长和提高GA-SVR模型预测精度。     

Flip chip on board solder joint reliability analysis using 2-D and3-D FEA models

This study investigates the effects of employing different two-dimensional (2-D) and three-dimensional (3-D) finite element analysis (FEA) models for analyzing the solder joint reliability performance of a flip chip on board assembly. The FEA models investigated were the 2-D-plane strain, 2-D-plane stress, 3-D-1/8th symmetry and 3-D-strip models. The different stress and strain responses generated by the four different FEA models were applied to various solder joint low cycle fatigue life prediction relationships. The investigation shows that the 2-D-plane strain and 2-D-plane stress models gave the highest and lowest solder joint strains, respectively. The 3-D-strip and 3-D-1/8th symmetry model results fall in between the 2-D-plane strain and 2-D-plane stress model results. The 3-D-1/8th symmetry model agrees better with the 2-D-plane strain model, while the 3-D-strip model agrees better with the 2-D-plane stress model results. The results for the fatigue life prediction analyses also show similar trends