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.     

Two-dimensional correlation analysis for a kinetic model of consecutive reactions

We have systematically studied a kinetic scheme of consecutive reactions by using generalized two-dimensional (2D) correlation analysis as reported by Noda. The correlations between reactant-intermediate, intermediate-product, and reactant-product pairs are analyzed with the related rate constants and absorption coefficients. When the reference spectrum is set at zero, the synchronous and asynchronous correlation spectra for the kinetic model are almost free from the influence of poor quality signals. If an appropriate reference spectrum is selected, the intermediate can be feasibly distinguished from other species involved in the reaction. A ratio of asynchronous to synchronous correlation intensity yields a coherence spectrum, which is characterized by different plateau-type peak intensities. When a steady-state condition fits the kinetic model, the peak summation of reactant-intermediate and intermediate-product correlation will approach the intensity of the reactant-product correlation. The coherence spectrum is useful for pattern recognition of the reaction scheme and also provides an effective way to identify the location and the extent of spectral overlap between two peaks.     

A Bayesian method for long AR spectral estimation: a comparativestudy

We address the problem of smooth power spectral density estimation of zero-mean stationary Gaussian processes when only a short observation set is available for analysis. The spectra are described by a long autoregressive model whose coefficients are estimated in a Bayesian regularized least squares (RLS) framework accounting the spectral smoothness prior. The critical computation of the tradeoff parameters is addressed using both maximum likelihood (ML) and generalized cross-validation (GCV) criteria in order to automatically tune the spectral smoothness. The practical interest of the method is demonstrated by a computed simulation study in the field of Doppler spectral analysis. In a Monte Carlo simulation study with a known spectral shape, investigation of quantitative indexes such as bias and variance, but also quadratic, logarithmic, and Kullback distances shows interesting improvements with respect to the usual least squares method, whatever the window data length and the signal-to-noise ratio (SNR)     

响应面法在结构体系可靠度分析中的应用

一个失效模式由许多的失效单元构成,它是一个并联系统;而所有的失效模式构成一个串联系统。整个结构体系可看成是许多并联系统(失效模式)组成的一个串联系统。首先,利用基于响应面的随机有限元法来获得失效模式中各个单元的极限状态方程,这些方程都是二次多项式;第二步,利用结构可靠度分析中的几何法得到这些方程的等效线性化方程从而可逐步得到该失效模式的等效线性化方程;第三步,计算各失效模式间的相关系数;最后,由Ditlevsen界限法来计算结构的体系可靠度。算例表明,利用该方法来获得大型、复杂结构的体系可靠度具有高效、实用的特点。     

Spectral color constancy using a maximum entropy approach

This paper proposes a solution to the spectral color constancy problem. The method is based on a statistical model for the surface reflectance spectrum and applies a maximum entropy constraint. Unlike prior methods based on linear models, the solution process does not require a set of basis functions to be defined, nor does it require a database of spectra to be specified in advance. Experiments on simulated and real data show that spectral estimation using the maximum entropy approach is feasible and performs similarly to existing spectral methods in spite of the lower level of a priori information required.     

Charger: combination of signal processing and statistical learning algorithms for precursor charge-state determination from electron-transfer dissociation spectra

Tandem mass spectrometry in combination with liquid chromatography has emerged as a powerful tool for characterization of complex protein mixtures in a high-throughput manner. One of the bioinformatics challenges posed by the mass spectral data analysis is the determination of precursor charge when unit mass resolution is used for detecting fragment ions. The charge-state information is used to filter database sequences before they are correlated to experimental data. In the absence of the accurate charge state, several charge states are assumed. This dramatically increases database search times. To address this problem, we have developed an approach for charge-state determination of peptides from their tandem mass spectra obtained in fragmentations via electron-transfer dissociation (ETD) reactions. Protein analysis by ETD is thought to enhance the range of amino acid sequences that can be analyzed by mass spectrometry-based proteomics. One example is the improved capability to characterize phosphorylated peptides. Our approach to charge-state determination uses a combination of signal processing and statistical machine learning. The signal processing employs correlation and convolution analyses to determine precursor masses and charge states of peptides. We discuss applicability of these methods to spectra of different charge states. We note that in our applications correlation analysis outperforms the convolution in determining peptide charge states. The correlation analysis is best suited for spectra with prevalence of complementary ions. It is highly specific but is dependent on quality of spectra. The linear discriminant analysis (LDA) approach uses a number of other spectral features to predict charge states. We train LDA classifier on a set of manually curated spectral data from a mixture of proteins of known identity. There are over 5000 spectra in the training set. A number of features, pertinent to spectra of peptides obtained via ETD reactions, have been used in the training. The loading coefficients of LDA indicate the relative importance of different features for charge-state determination. We have applied our model to a test data set generated from a mixture of 49 proteins. We search the spectra with and without use of the charge-state determination. The charge-state determination helps to significantly save the database search times. We discuss the cost associated with the possible misclassification of charge states.     

Value function approximation via linear programming for FMS scheduling

In this paper, we develop a linear programming framework for computing a quadratic approximation to the value function, which constitutes the off-line computation of a hierarchical FMS scheduling approach previously developed by us. In contrast to previous work, where relatively crude value functions were used, we develop a quadratic approximation that is a prior fit. We consider the multiple part multiple machine discounted cost case and illustrate the approach via a simulation example in the context of an industrial setting.     

A min-norm approach for estimating phase distribution in an interferogram

Phase distribution in an interferogram is usually computed from several phase shifted intensity images acquired temporally by means of a CCD camera. These phase shifts are commonly accomplished by translation of a mirror with a piezoelectric transducer (PZT). In reality the PZT motion is not exact. Thus the aim of this paper is to present a novel approach for estimating the phase steps that are imparted to the PZT in the presence of nonsinusoidal waveforms and random noise. The method functions by designing an autocovariance matrix from the intensity registered on the CCD for N data frames. The eigendecomposition of an autocovariance matrix yields the signal and noise subspaces. The phase step values are estimated pixelwise from the noise subspace. This approach provides the flexibility of using arbitrary phase steps, a feature most commonly attributed to generalized phase shifting algorithms. Once the phase steps are estimated the Vandermonde system of equations is applied to estimate the phase distribution.     

Efficient uncertainty propagation for network multiphysics systems

We consider a multiphysics system with multiple component PDE models coupled together through network coupling interfaces, that is, a handful of scalars. If each component model contains uncertainties represented by a set of parameters, a straightforward uncertainty quantification study would collect all uncertainties into a single set and treat the multiphysics model as a black box. Such an approach ignores the rich structure of the multiphysics system, and the combined space of uncertainties can have a large dimension that prohibits the use of polynomial surrogate models. We propose an intrusive methodology that exploits the structure of the network coupled multiphysics system to efficiently construct a polynomial surrogate of the model output as a function of uncertain inputs. Using a nonlinear elimination strategy, we treat the solution as a composite function: the model outputs are functions of the coupling terms, which are functions of the uncertain parameters. The composite structure allows us to construct and employ a reduced polynomial basis that depends on the coupling terms. The basis can be constructed with many fewer PDE solves than the naive approach, which results in substantial computational savings. We demonstrate the method on an idealized model of a nuclear reactor. Copyright © 2014 John Wiley & Sons, Ltd.     

Data-driven approach for metabolite relationship recovery in biological 1H NMR data sets using iterative statistical total correlation spectroscopy

Statistical total correlation spectroscopy (STOCSY) is a well-established and valuable method in the elucidation of both inter- and intrametabolite correlations in NMR metabonomic data sets. Here, the STOCSY approach is extended in a novel Iterative-STOCSY (I-STOCSY) tool in which correlations are calculated initially from a driver peak of interest and subsequently for all peaks identified as correlating with a correlation coefficient greater than a set threshold. Consequently, in a single automated run, the majority of information contained in multiple STOCSY calculations from all peaks recursively correlated to the original user defined driver peak of interest are recovered. In addition, highly correlating peaks are clustered into putative structurally related sets, and the results are presented in a fully interactive plot where each set is represented by a node; node-to-node connections are plotted alongside corresponding spectral data colored by the strength of connection, thus allowing the intuitive exploration of both inter- and intrametabolite connections. The I-STOCSY approach has been here applied to a (1)H NMR data set of 24 h postdose aqueous liver extracts from rats treated with the model hepatotoxin galactosamine and has been shown both to recover the previously deduced major metabolic effects of treatment and to generate new hypotheses even on this well-studied model system. I-STOCSY, thus, represents a significant advance in correlation based analysis and visualization, providing insight into inter- and intrametabolite relationships following metabolic perturbations.     

On the accuracy and limits of peptide fragmentation spectrum prediction

We estimated the reproducibility of tandem mass spectra for the widely used collision-induced dissociation (CID) of peptide ions. Using the Pearson correlation coefficient as a measure of spectral similarity, we found that the within-experiment reproducibility of fragment ion intensities is very high (about 0.85). However, across different experiments and instrument types/setups, the correlation decreases by more than 15% (to about 0.70). We further investigated the accuracy of current predictors of peptide fragmentation spectra and found that they are more accurate than the ad-hoc models generally used by search engines (e.g., SEQUEST) and, surprisingly, approaching the empirical upper limit set by the average across-experiment spectral reproducibility (especially for charge +1 and charge +2 precursor ions). These results provide evidence that, in terms of accuracy of modeling, predicted peptide fragmentation spectra provide a viable alternative to spectral libraries for peptide identification, with a higher coverage of peptides and lower storage requirements. Furthermore, using five data sets of proteome digests by two different proteases, we find that PeptideART (a data-driven machine learning approach) is generally more accurate than MassAnalyzer (an approach based on a kinetic model for peptide fragmentation) in predicting fragmentation spectra but that both models are significantly more accurate than the ad-hoc models.     

Sign constraints improve the detection of differences between complex spectral data sets: LC-IR as an example

Spectroscopy is a fast and rich analytical tool. On many occasions, spectra are acquired of two or more sets of samples that differ only slightly. These data sets then need to be compared and analyzed, but sometimes it is difficult to find the differences. We present a simple and effective method that detects and extracts new spectral features in a spectrum coming from one set with respect to spectra of another set on the basis of the fact that these new spectral features are essentially positive quantities. The proposed procedure (i) characterizes the spectra of the reference set by a component model and (ii) uses asymmetric least squares (ASLS) to find differences with respect to this component model. It should be stressed that the method only focuses on new features and does not trace relative changes of spectral features that occur in both sets of spectra. A comparison is made with the conventional ordinary least squares (OLS) approach. Both methods (OLS and ASLS) are illustrated with simulations and are tested for size-exclusion chromatography with infrared detection (SEC-IR) of mixtures of polymer standards. Both methods are able to provide information about new spectral features. It is shown that the ASLS-based procedure yields the best recovery of new features in the simulations and in the SEC-IR experiments. Band positions and band shapes of new spectral features are better retrieved with the ASLS than with the OLS method, even those which could hardly be detected visually. Depending on the spectroscopic technique used, the ASLS-based method facilitates identification of the new chemical compounds.     

Uniform rational approximation of functions of several variables

We present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.     

Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems

The Abbe sine condition and the recently developed pupil astigmatism conditions provide a powerful set of relationships for describing imaging systems that are free from aberrations that have linear and quadratic dependence on field, to all orders in the pupil. We have proved both of these conditions and applied them to axisymmetric imaging systems. We now extend our approach to plane-symmetric systems. Still using Hamilton's characteristic functions, we derive the general sine conditions and the pupil astigmatism conditions that describe plane-symmetric systems that are free of all aberrations with linear and quadratic field dependence.     

基于Lorenz混沌调频的水下正交波形集设计

针对网络水下航行器组联合探测情况下各网络节点间信号会互相干扰的问题,基于Lorenz混沌模型,提出一种混沌调频(Chaos Frequency Modulation,CFM)的正交波形集设计方法。首先建立基于Lorenz序列的CFM信号模型,对其进行相关特性分析和正交特性研究,包括CFM正交波形集的个数和波形长度对波形集正交性能的影响,提出对混沌序列进行加窗函数处理的CFM波形集正交性优化方法;然后构造网络水下航行器组分别发射线性调频(Linear Frequency Modulation,LFM)信号和CFM信号的回波模型,对比分析了匹配滤波器对回波信号的处理结果。仿真结果表明,该设计方法简便、灵活、高效,产生的CFM正交波形集性能良好,且相对于常规信号在水下信号检测方面具有明显的优势。     

Data interpretation for spectral sensors with correlated bands

New classes of spectral sensors are emerging that have significant overlap in the band spectral response functions. While conventional sensors such as the Multispectral Thermal Images (MTI) or Landsat may have responses with a few percent overlap between adjacent bands, some of the emerging sensors can have more than 50% correlation among all spectral bands. The traditional geometrical models used to describe spectral data fail when such high levels of correlation exist. In this paper we present a generalized geometrical model that relies on functional analysis. We define a sensor space and a scene space that can be used to characterize the suitability of a sensor for a particular spectral sensing task. We demonstrate that classifiers based on first-order distance and angle metrics fail for sensors with highly correlated bands unless appropriate preprocessing is carried out. We further show that second-order statistical classifiers are largely immune to many of the problems introduced by the correlated band responses.     

Galerkin finite element methods for wave problems

We compare here the accuracy, stability and wave propagation properties of a few Galerkin methods. The basic Galerkin methods with piecewise linear basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) have been compared with the streamwise-upwind Petrov Galerkin (SUPG) method for their ability to solve wave problems. It is shown here that when the piecewise linear basis functions are replaced by quadratic polynomials, the stencils become much larger (involving five overlapping elements), with only a very small increase in spectral accuracy. It is also shown that all the three Galerkin methods have restricted ranges of wave numbers and circular frequencies over which the numerical dispersion relation matches with the physical dispersion relation — a central requirement for wave problems. The model one-dimensional convection equation is solved with a very fine uniform grid to show the above properties. With the help of discontinuous initial condition, we also investigate the Gibbs’ phenomenon for these methods.     

Constrained quadratic correlation filters for target detection

A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented.     

Hybrid clustering of multi-view data via Tucker-2 model and its application

With the modern technology fast developing, most of entities can be observed by different perspectives. These multiple view information allows us to find a better pattern as long as we integrate them in an appropriate way. So clustering by integrating multi-view representations that describe the same class of entities has become a crucial issue for knowledge discovering. We integrate multi-view data by a tensor model and present a hybrid clustering method based on Tucker-2 model, which can be regarded as an extension of spectral clustering. We apply our hybrid clustering method to scientific publication analysis by integrating citation-link and lexical content. Clustering experiments are conducted on a large-scale journal set retrieved from the Web of Science (WoS) database. Several relevant hybrid clustering methods are cross compared with our method. The analysis of clustering results demonstrate the effectiveness of the proposed algorithm. Furthermore, we provide a cognitive analysis of the clustering results as well as the visualization as a mapping of the journal set.