Weighted compression of spectral color information

Spectral color information is used nowadays in many different applications. Accurate spectral images are usually very large files, but a proper compression method can reduce needed storage space remarkably with a minimum loss of information. In this paper we introduce a principal component analysis (PCA) -based compression method of spectral color information. In this approach spectral data is weighted with a proper weight function before forming the correlation matrix and calculating the eigenvector basis. First we give a general framework for how to use weight functions in compression of relevant color information. Then we compare the weighted compression method with the traditional PCA compression method by compressing and reconstructing the Munsell data set consisting of 1,269 reflectance spectra and the Pantone data set consisting of 922 reflectance spectra. Two different weight functions are proposed and tested. We show that weighting clearly improves retention of color information in the PCA-based compression process.     

Extension of quadrature orthogonal signal corrected two-dimensional (QOSC 2D) correlation spectroscopy I: principal component analysis based QOSC 2D

The present study proposes a new quadrature orthogonal signal correlation (QOSC) filtering method based on principal component analysis (PCA). The external perturbation variable vector typically used in the QOSC operation is replaced with a matrix consisting of the spectral data principal components (PCs) and their quadrature counterparts obtained by using the discrete Hilbert-Noda transformation. Thus, QOSC operation can be carried out for a dataset without the explicit knowledge of the external variables information. The PCA-based QOSC filtering can be most effectively applied to two-dimensional (2D) correlation analysis. The performance of this filtering operation on the simulated spectra data set with the interference of strong random noise demonstrated that the PCA-based QOSC filtering not only eliminates the influence of signals that are unrelated to the final target but also preserves the out-of-phase information in the data matrix essential for asynchronous correlation analysis. The result of 2D correlation analysis has also demonstrated that essentially only one principal component is necessary for PCA-based QOSC to perform well. Although the present PCA-based QOSC filtering scheme is not as powerful as that based on the explicit knowledge of the external variable vector, it still can significantly improve the quality of 2D correlation spectra and enables OSC 2D to deal with the problems of losing the quadrature (or out-of-phase) information. In particular, it opens a way to perform QOSC for the spectral dataset without external variables information. The proposed approach should have wide applications in 2D correlation analysis of spectra driven by multiplicative effects in complicated systems in biological, pharmaceutical, and agriculture fields, and so on, where the explicit nature of the external perturbation cannot always be known.     

Spectral-reflectance reconstruction in the near-infrared region by use of conventional charge-coupled-device camera measurements

Our aim is to develop a method for obtaining the reflectance spectra of samples in the near-infrared (NIR) region (800-1,000 nm) by using a small number of measurements performed with a conventional CCD camera (multispectral imaging). We experimentally determined the spectral sensitivity of the CCD camera in the NIR range, used a method based on principal component analysis to reconstruct the spectral reflectance of the samples, and analyzed the number and shape of the filters that need tobe used to apply this method. Finally we obtained the reflectance spectra of a set of 30 spectral curves by numerical simulation. The small amount of errors in the spectral reconstruction shows the potential of this method for reconstructing spectral reflectances in the NIR range.     

Multivariate statistical diagnosis using triangular representation of fault patterns in principal component space

A pattern‐based multivariate statistical diagnosis method is proposed to diagnose a process fault on‐line. A triangular representation of process trends in the principal component space is employed to extract the on‐line fault pattern. The extracted fault pattern is compared with the existing fault patterns stored in the fault library. A diagnostic decision is made based on the similarity between the extracted and the existing fault patterns, called a similarity index. The diagnosis performance of the proposed method is demonstrated using simulated data from Tennessee Eastman process. The diagnosis success rate and robustness to noise of the proposed method are also discussed via computational experiments.     

Gaussian process regression for multivariate spectroscopic calibration

Traditionally multivariate calibration models have been developed using regression based techniques including principal component regression and partial least squares and their non-linear counterparts. This paper proposes the application of Gaussian process regression as an alternative method for the development of a calibration model. By formulating the regression problem in a probabilistic framework, a Gaussian process is derived from the perspective of Bayesian non-parametric regression, prior to describing its implementation using Markov chain Monte Carlo methods. The flexibility of a Gaussian process, in terms of the parameterization of the covariance function, results in its good performance in terms of the development of a calibration model for both linear and non-linear data sets. To handle the high dimensionality of spectral data, principal component analysis is initially performed on the data, followed by the application of Gaussian process regression to the scores of the extracted principal components. In this sense, the proposed method is a non-linear variant of principal component regression. The effectiveness of the Gaussian process approach for the development of a calibration model is demonstrated through its application to two spectroscopic data sets. A statistical hypothesis test procedure, the paired t-test, is used to undertake an empirical comparison of the Gaussian process approach with conventional calibration techniques, and it is concluded that the Gaussian process exhibits enhanced behaviour.     

Fault diagnosis of batch processes using discriminant model

A new statistical online diagnosis method for a batch process is proposed. The proposed method consists of two phases: offline model building and online diagnosis. The offline model building phase constructs an empirical model, called a discriminant model, using various past batch runs. When a fault of a new batch is detected, the online diagnosis phase is initiated. The behaviour of the new batch is referenced against the model, developed in the offline model building phase, to make a diagnostic decision. The diagnosis performance of the proposed method is tested using a dataset from a PVC batch process. It has been shown that the proposed method outperforms existing PCA-based diagnosis methods, especially at the onset of a fault.     

Removal of analyte-irrelevant variations in near-infrared tissue spectra

This paper describes mathematical techniques to correct for analyte-irrelevant optical variability in tissue spectra by combining multiple preprocessing techniques to address variability in spectral properties of tissue overlying and within the muscle. A mathematical preprocessing method called principal component analysis (PCA) loading correction is discussed for removal of inter-subject, analyte-irrelevant variations in muscle scattering from continuous-wave diffuse reflectance near-infrared (NIR) spectra. The correction is completed by orthogonalizing spectra to a set of loading vectors of the principal components obtained from principal component analysis of spectra with the same analyte value, across different subjects in the calibration set. Once the loading vectors are obtained, no knowledge of analyte values is required for future spectral correction. The method was tested on tissue-like, three-layer phantoms using partial least squares (PLS) regression to predict the absorber concentration in the phantom muscle layer from the NIR spectra. Two other mathematical methods, short-distance correction to remove spectral interference from skin and fat layers and standard normal variate scaling, were also applied and/or combined with the proposed method prior to the PLS analysis. Each of the preprocessing methods improved model prediction and/or reduced model complexity. The combination of the three preprocessing methods provided the most accurate prediction results. We also performed a preliminary validation on in vivo human tissue spectra.     

Automatic feature selection for unsupervised clustering of cycle-based signals in manufacturing processes

Recent developments in sensing and computer technology have resulted in most manufacturing processes becoming a data-rich environment. A cycle-based signal refers to an analog or digital signal that is obtained during each repetition of an operation cycle in a manufacturing process. It is a very important class of in-process sensing signals for manufacturing processes because it contains extensive information on the process condition and product quality (e.g., the forming force signal in forging processes). In contrast with currently available supervised classification approaches that heavily depend on the training dataset or engineering field knowledge, this paper aims to develop an automatic feature selection method for the unsupervised clustering of cycle-base signals. First, principal component analysis is applied to the raw signals. Then a new method is proposed to select information containing principal components to allow clustering to be performed. The dimension of the problem can be significantly reduced through the use of these two steps. Finally, a model-based clustering method is applied to the selected principal components to find the clusters in the cycle-based signals. A numerical example and a real-world example of a forging process are used to illustrate the effectiveness of the proposed method. The proposed technique is an important data pre-processing technique for the monitoring and diagnostic system development using cycle-based signals for manufacturing processes.     

Comparative study of face recognition techniques that use joint transform correlation and principal component analysis

Face recognition based on principal component analysis (PCA) that uses eigenfaces is popular in face recognition markets. We present a comparison between various optoelectronic face recognition techniques and a PCA-based technique for face recognition. Computer simulations are used to study the effectiveness of the PCA-based technique, especially for facial images with a high level of distortion. Results are then compared with various distortion-invariant optoelectronic face recognition algorithms such as synthetic discriminant functions (SDF), projection-slice SDF, optical-correlator-based neural networks, and pose-estimation-based correlation.     

面向高保真再现的多光谱图像降维方法

目的研究满足面向高保真再现要求的多光谱图像降维方法。方法基于二进制小波对信号的分解与人类的视觉特性相匹配,以及非负主成分分析法可较好地保证降维的光谱精度,提出采用基于离散二进制小波变化与非负主成分分析法的综合降维方法,并基于多光谱图像高保真再现的光谱精度、色度精度与变光源色差稳定性的要求,提出采用CIELAB的标准色差ab?E、光谱保真度和平均梯度等3个指标来评价降维效果。结果经过多光谱图像的测试实验,基于离散小波变换和非负主成分分析法的综合降维方法相对于其他3种方法,其光谱精度、色度精度和图像清晰度保持良好。结论该方法较好地实现了多光谱图像的高保真再现问题,并且为颜色视觉的认知过程提供了新的理论解释。     

Third harmonic transmit phasing for tissue harmonic generation

Generation of tissue harmonic signals during acoustic propagation is based on the combined effect of two different spectral interactions of the transmit signal. One produces harmonic whose frequency is the sum of transmit frequencies. The other results in harmonic at difference frequency of the transmit signals. Both the frequency-sum component and the frequency-difference component are sensitive to the phase of their constitutive spectral signals. In this study, a novel approach for modifying the amplitude of tissue harmonic signal is proposed based on phasing these two components to achieve either harmonic enhancement or suppression. Both experiments and simulations were performed to investigate the effects of 3f0 transmit phasing on tissue harmonic generation. Results indicate that the relative phasing between the frequency-sum component and the frequency-difference component markedly changes the amplitude of the second harmonic signal. For harmonic enhancement, approximate 6 dB increase of second harmonic amplitude can be achieved while the lateral harmonic beam pattern also is improved as compared to conventional situations in which only the frequency-sum component is considered. For harmonic suppression, the second harmonic signal also could be significantly reduced by about 11 dB when the frequency-difference component is out of phase with the frequency-sum component. Hence, the method of 3f0 transmit phasing has potentials for both improving signal-to-noise ratio in tissue harmonic imaging and enhancing image contrast in contrast-agent imaging by suppression of tissue harmonic background.     

Sensor fault identification based on time-lagged PCA in dynamic processes

Principal component analysis (PCA) is widely employed as a multivariate statistical method for fault detection, isolation and diagnosis in chemical processes. Previously, PCA has been successfully used to identify faulty sensors under normal static operating conditions. In this paper, we extend the reconstruction-based sensor fault isolation method proposed by Dunia et al. to dynamic processes. We develop a new method for identifying and isolating sensor faults in an inherent dynamic system. First, we describe how to reconstruct noisy or faulty measurements in dynamic processes. The reconstructed measurements are obtained by simple iterative optimization based on the correlation structure of the time-lagged data set. Then, based on the sensor validity index (SVI) approach developed by Dunia et al., we propose an SVI for fault isolation in dynamic processes. The proposed method was applied to sensor fault isolation in two strongly dynamic systems: a simulated 4×4 dynamic process and a simulated wastewater treatment process (WWTP). In these experiments, the proposed sensor fault identification method correctly and rapidly identified the faulty sensor; in contrast, the traditional PCA-based sensor fault isolation approach showed unsatisfactory results when applied to the same systems.     

遗传算法加权中值滤波器的优化设计

当测试数据中随机干扰满足高斯分布时,可以采用线性滤波器进行信号处理得到所要求的有用信号.而当随机干扰为非高斯分布时,则必须采用非线性的信号处理方法才能获得所要求的有用信号.这里讨论一类非线性滤波器——加权中值滤波器的最优设计问题.取损失函数为绝对误差的数学期望值,采用实数值编码多子种群的标准遗传算法来极小化损失函数.由于遗传算法:是用点群进行寻优,而不是用一个单点进行寻优,具有隐含并行算法的特点;群体在每一代的进化过程中执行同样的复制、交叉、变异操作,仅使用问题本身所对应的适应度函数,而不需要任何其它先决条件或辅助信息;遗传算法使用随机转换规则,而不是确定性规则进行运算.遗传算法作为一类全局最优算法,它所得到的加权中值滤波器也是全局最优的.数值计算结果表明,采用遗传算法可以得到更小的绝对误差平均值,且优于LMA算法.     

基于维纳估计的光谱反射率重建优化算法研究

目的研究光谱反射率重建算法,解决各种物体颜色的光谱反射率重建精度问题。方法通过高精度多光谱成像系统获取实验样本的系统响应值,分光光度计获取样本的光谱反射率,采用Wiener估计法、自适应维纳估计法和提出的优化维纳估计法,对待测样本实验数据进行光谱重建,并评价重建结果。结果在3种光谱重建算法仿真实验中,提出算法的均方根误差平均值为0.0355,平均CIE1976色差为1.4349,优于其他2种算法。结论在光谱重建算法的研究中,基于优化的维纳估计算法可以有效提高光谱的重建精度,可应用于实际的多光谱成像复制中。     

A unified statistical framework for monitoring multivariate systems with unknown source and error signals

This article proposes a unified multivariate statistical monitoring framework that incorporates recent work on maximum likelihood PCA (MLPCA) into conventional PCA-based monitoring. The proposed approach allows the simultaneous and consistent estimation of the PCA model plane, its dimension and the error covariance matrix. This paper also invokes recent work on monitoring non-Gaussian processes to extract unknown Gaussian as well as non-Gaussian source signals from recorded process data. By contrasting the unified framework with PCA-based process monitoring using a simulation example and recorded data from two industrial processes, the proposed approach produced more accurate and/or sensitive monitoring models.     

New method for spectral data classification: two-way moving window principal component analysis

Two-way moving window principal component analysis (TMWPCA), which considers all possible variable regions by using variable and sample moving windows, is proposed as a new spectral data classification method. In TMWPCA, the similarity between model function and the index obtained by variable and sample moving windows is defined as "fitness". For each variable region selected by a variable moving window, the fitness is obtained through the use of a model function. By maximizing the fitness, an optimal variable region can be searched. A remarkable advantage of TMWPCA is that it offers an optimal variable region for the classification. To demonstrate the potential of TMWPCA, it has been applied to the classification of visible-near-infrared (Vis-NIR) spectra of mastitic and healthy udder quarters of cows measured in a nondestructive manner. The misclassification rate of TMWPCA has been compared with those of other chemometric methods, such as principal component analysis (PCA), soft independent modeling of class analogies (SIMCA), and principal discriminant variate (PDV). TMWPCA has yielded the lowest misclassification rate. The result indicates that TMWPCA is a powerful tool for the classification of spectral data.     

Multivariate optical computation for predictive spectroscopy

A novel optical approach to predicting chemical and physical properties based on principal component analysis (PCA) is proposed and evaluated using a data set from earlier work. In our approach, a regression vector produced by PCA is designed into the structure of a set of paired optical filters. Light passing through the paired filters produces an analog detector signal that is directly proportional to the chemical/physical property for which the regression vector was designed. This simple optical computational method for predictive spectroscopy is evaluated in several ways, using the example data for numeric simulation. First, we evaluate the sensitivity of the method to various types of spectroscopic errors commonly encountered and find the method to have the same susceptibilities toward error as standard methods. Second, we use propagation of errors to determine the effects of detector noise on the predictive power of the method, finding the optical computation approach to have a large multiplex advantage over conventional methods. Third, we use two different design approaches to the construction of the paired filter set for the example measurement to evaluate manufacturability, finding that adequate methods exist to design appropriate optical devices. Fourth, we numerically simulate the predictive errors introduced by design errors in the paired filters, finding that predictive errors are not increased over conventional methods. Fifth, we consider how the performance of the method is affected by light intensities that are not linearly related to chemical composition (as in transmission spectroscopy) and find that the method is only marginally affected. In summary, we conclude that many types of predictive measurements based on use of regression (or other) vectors and linear mathematics can be performed more rapidly, more effectly, and at considerably lower cost by the proposed optical computation method than by traditional dispersive or interferometric instrumentation. Although our simulations have used Raman experimental data, the method is equally applicable to Near-IR, UV-vis, IR, fluorescence, and other spectroscopies.     

Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra

Nonnegative color analysis filters are obtained by using an invertible linear transformation of characteristic spectra, which are orthogonal vectors from a principal component analysis (PCA) of a representative ensemble of color spectra. These filters maintain the optimal compression properties of the PCA scheme. Linearly constrained nonlinear programming is used to find a transformation that minimizes the noise sensitivity of the filter set. The method is illustrated by computing analysis and synthesis filters for an ensemble of measured Munsell color spectra.     

Adaptive clutter filtering based on sparse component analysis in ultrasound color flow imaging

An adaptive method based on the sparse component analysis is proposed for stronger clutter filtering in ultrasound color flow imaging (CFI). In the present method, the focal underdetermined system solver (FOCUSS) algorithm is employed, and the iteration of the algorithm is based on weighted norm minimization of the dependent variable with the weights being a function of the preceding iterative solutions. By finding the localized energy solution vector representing strong clutter components, the FOCUSS algorithm first extracts the clutter from the original signal. However, the different initialization of the basis function matrix has an impact on the filtering performance of FOCUSS algorithms. Thus, 2 FOCUSS clutter- filtering methods, the original and the modified, are obtained by initializing the basis function matrix using a predetermined set of monotone sinusoids and using the discrete Karhunen-Loeve transform (DKLT) and spatial averaging, respectively. Validation of 2 FOCUSS filtering methods has been performed through experimental tests, in which they were compared with several conventional clutter filters using simplistic simulated and gathered clinical data. The results demonstrate that 2 FOCUSS filtering methods can follow signal varying adaptively and perform clutter filtering effectively. Moreover, the modified method may obtain the further improved filtering performance and retain more blood flow information in regions close to vessel walls.