Sampling and reconstruction of a checkerboard-type random field

A statistical procedure for sampling and reconstructing realizations of a random binary field is developed. The realizations are formed by using two binary Markovian processes defined on two axes. The procedure includes two parts. The first part is the choice of a sampling interval on the basis of a given probability of missing a state. The second part is to construct an estimator for the state transition points and to evaluate the variance of the estimator. The issue of the uncertainty of the initial state is resolved, which arises because the values of the generating processes are nonuniquely determined by field measurements. Illustrative examples are given.     

Random field modeling with insufficient field data for probability analysis and design

Often engineered systems entail randomness as a function of spatial (or temporal) variables. The random field can be found in the form of geometry, material property, and/or loading in engineering products and processes. In some applications, consideration of the random field is a key to accurately predict variability in system performances. However, existing methods for random field modeling are limited for practical use because they require sufficient field data. This paper thus proposes a new random field modeling method using a Bayesian Copula that facilitates the random field modeling with insufficient field data and applies this method for engineering probability analysis and robust design optimization. The proposed method is composed of three key ideas: (i) determining the marginal distribution of random field realizations at each measurement location, (ii) determining optimal Copulas to model statistical dependence of the field realizations at different measurement locations, and (iii) modeling a joint probability density function of the random field. A mathematical problem was first employed for the purpose of demonstrating the accuracy of the random field modeling with insufficient field data. The second case study deals with the assembly process of a two-door refrigerator that challenges predicting the door assembly tolerance and minimizing the tolerance by designing the random field and parameter variables in the assembly process with insufficient random field data. It is concluded that the proposed random field modeling can be used to successfully conduct the probability analysis and robust design optimization with insufficient random field data.     

Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators

This paper deals with the construction of a class of non-Gaussian positive-definite matrix-valued random fields whose mathematical properties allow elliptic stochastic partial differential operators to be modeled. The properties of this class is studied in details and the numerical procedure for constructing numerical realizations of the trajectories is explicitly given. Such a matrix-valued random field can directly be used for modeling random uncertainties in computational sciences with a stochastic model having a small number of parameters. The class of random fields which can be approximated is presented and their experimental identification is analyzed. An example is given in three-dimensional linear elasticity for which the fourth-order elasticity tensor-valued random field is constructed for a random non-homogeneous anisotropic elastic material.     

Measuring homogeneity of planar point-patterns by using kurtosis

Kurtosis is generally associated with measurements of peakedness of a distribution. In this paper, we suggest a method where kurtosis can be used as a measure of homogeneity of any quantifiable property on a planar surface. A 2-dimensional, continuous and uniform distribution has kurtosis equal to 5.6. This value is also the limiting value for a discrete uniform distribution defined on a regular, rectangular grid when the number of grid points tend to infinity. Measurements of a planar surface, taken at regular grid points, are considered as realizations of random fields. These are associated with 2-dimensional random variables from which the value of kurtosis can be computed and used as a measure of the homogeneity of the field. A deviation from 5.6 indicates that the stochastic variable is not uniformly distributed and that the corresponding random field is not homogeneous. The model is applied on the spatial variation of the roughness on the surface of newsprint, an application where homogeneity is very important.     

An MRF-Based Approach to Generation of Super-Resolution Images from Blurred Observations

This paper presents a new technique for generating a high resolution image from a blurred image sequence; this is also referred to as super-resolution restoration of images. The image sequence consists of decimated, blurred and noisy versions of the high resolution image. The high resolution image is modeled as a Markov random field (MRF) and a maximum a posteriori (MAP) estimation technique is used for super-resolution restoration. Unlike other super-resolution imaging methods, the proposed technique does not require sub-pixel registration of given observations. A simple gradient descent method is used to optimize the functional. The discontinuities in the intensity process can be preserved by introducing suitable line processes. Superiority of this technique to standard methods of image expansion like pixel replication and spline interpolation is illustrated.     

Robust structure from motion with affine camera via low-rank matrix recovery

We present a novel approach to structure from motion that can deal with missing data and outliers with an affine camera. We model the corruptions as sparse error. Therefore the structure from motion problem is reduced to the problem of recovering a low-rank matrix from corrupted observations. We first decompose the matrix of trajectories of features into low-rank and sparse components by nuclear-norm and l1-norm minimization, and then obtain the motion and structure from the low-rank components by the classical factorization method. Unlike pervious methods, which have some drawbacks such as depending on the initial value selection and being sensitive to the large magnitude errors, our method uses a convex optimization technique that is guaranteed to recover the low-rank matrix from highly corrupted and incomplete observations. Experimental results demonstrate that the proposed approach is more efficient and robust to large-scale outliers.     

Generating Fluttering Patterns with Low Autocorrelation for Coded Exposure Imaging

The performance of coded exposure imaging critically depends on finding good binary sequences. Previous coded exposure imaging methods have mostly relied on random searching to find the binary codes, but that approach can easily fail to find good long sequences, due to the exponentially expanding search space. In this paper, we present two algorithms for generating the binary sequences, which are especially well suited for generating short and long binary sequences, respectively. We show that the concept of low autocorrelation binary sequences, which has been successfully exploited in the field of information theory, can be applied to generate shutter fluttering patterns. We also propose a new measure for good binary sequences. Based on the new measure, we introduce two new algorithms for coded exposure imaging - a modified Legendre sequence method and a memetic algorithm. Experiments using both synthetic and real data show that our new algorithms consistently generate better binary sequences for the coded exposure problem, yielding better deblurring and resolution enhancement results compared to previous methods of generating the binary codes.     

Generating connected textured fractal patterns using Markov randomfields

An algorithm that yields textured and connected binary fractals is presented. The texture is imposed by modelling the fractal as a Markov random field (MRF) at every resolution level. The model size and the parameters specify the texture. The generation starts at a coarser level and continues at finer levels. Connectivity, which is a global property, is maintained by restricting the flow of the sample generating Markov chain within a limited subset of all possible outcomes of the Markov random field. The texture is controlled by the parameters of the MRF model being used. Sample patterns are shown     

A super-resolution mapping method using local indicator variograms

Super-resolution mapping (SRM) is a recently developed research task in the field of remotely sensed information processing. It provides the ability to obtain land-cover maps at a finer scale using relatively low-resolution images. Existing algorithms based on indicator geostatistics and downscaling cokriging offer an SRM approach using spatial structure models derived from real data. In this article, a novel SRM method is developed based on a sequentially produced with local indicator variogram (SLIV) SRM model. In the SLIV method, indicator variograms extracted from target-resolution classification are produced from a representative local area as opposed to using the entire image. This simplifies the application of the method since limited target-resolution reference data are required. Our investigation on three diverse case studies shows that the local window (approximately 2% of the entire study area) selection process offers comparable accuracy results to those using globally derived spatial structures, indicating our methodology to be a promising practice. Furthermore, comparison of the proposed method with random realizations indicates an improvement of 7–12% in terms of overall accuracy and 15–18% in terms of the kappa coefficient. The evaluation focused on a 270–30 m pixel size reconstruction as a potential popular application, for example moving from Moderate Resolution Imaging Spectroradiometer (MODIS) to Landsat-type resolutions.     

Stochastic inverse method to identify parameter random fields in a structure

The parameters in a structure such as geometric and material properties are generally uncertain due to manufacturing tolerance, wear, fatigue and material irregularity. Such parameters are random fields because the uncertain properties vary along the spatial domain of a structure. Since the parameter uncertainties in a structure result in the uncertainty of the structural dynamic behavior, they need to be identified accurately for structural analysis or design. In order to identify the random fields of geometric parameters, the parameters can be measured directly using a 3-dimensional coordinate measuring machine. However, it is often very expensive to measure them directly. It is even impossible to directly measure some parameters such as density and Young’s modulus. For that case, the parameter random fields should be identified from measurable response data samples. In this paper, a stochastic inverse method to identify parameter random fields in a structure using modal data is proposed. The proposed method consists of the following three steps: (i) obtaining realizations of the parameter random field from modal data samples by solving an optimization problem, (ii) obtaining the deterministic terms in the Karhunen-Loève expansion by solving an eigenvalue problem and (iii) estimating the distributions of random variables in the Karhunen-Loève expansion using a maximum likelihood estimation method with kernel density.     

An approximation of random field with a bounded discrete parameter space

The model of n-dimensional random field with a bounded discrete parameter space is presented. To obtain simple method for generating random field with a computer it is assumed the field is Gaussian and Markovian. The special cases of two- and three-dimensional random fields are considered exactly. A numerical example is presented.     

Super-resolution land cover mapping with indicator geostatistics

Many satellite images have a coarser spatial resolution than the extent of land cover patterns on the ground, leading to mixed pixels whose composite spectral response consists of responses from multiple land cover classes. Spectral unmixing procedures only determine the fractions of such classes within a coarse pixel without locating them in space. Super-resolution or sub-pixel mapping aims at providing a fine resolution map of class labels, one that displays realistic spatial structure (without artifact discontinuities) and reproduces the coarse resolution fractions. In this paper, existing approaches for super-resolution mapping are placed within an inverse problem framework, and a geostatistical method is proposed for generating alternative synthetic land cover maps at the fine (target) spatial resolution; these super-resolution realizations are consistent with all the information available.More precisely, indicator coKriging is used to approximate the probability that a pixel at the fine spatial resolution belongs to a particular class, given the coarse resolution fractions and (if available) a sparse set of class labels at some informed fine pixels. Such Kriging-derived probabilities are used in sequential indicator simulation to generate synthetic maps of class labels at the fine resolution pixels. This non-iterative and fast simulation procedure yields alternative super-resolution land cover maps that reproduce: (i) the observed coarse fractions, (ii) the fine resolution class labels that might be available, and (iii) the prior structural information encapsulated in a set of indicator variogram models at the fine resolution. A case study is provided to illustrate the proposed methodology using Landsat TM data from SE China.     

Robust topology optimization accounting for spatially varying manufacturing errors

This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem.     

Role of remote sensing in flood management—the May 1990 cyclone

Temperature and composition profiles of the earth's atmosphere may be deduced from measurements of emitted thermal radiation made by satellite borne instruments. Such measurements have the advantage of continuous global coverage, but have poor vertical resolution compared with radio- and rocketsondes. The measured signals depend on weighted averages of the profiles over height so that the measurements are insensitive to fine scale structure. Conversely, fine scale structure in a profile retrieved from the radiances depends critically on the values of the measured radiances, which include an element of random noise; a balance has to be made between resolution and precision of the retrieved prolile. In this paper, linear system theory is applied to radiometers for atmospheric remote sensing. Fourier transform methods, commonly used in the analysis of time dependent or spatial signal processing systems, provide a quantitative relationship between vertical resolution and precision through the spatial wavenumber response function. Simplified atmospheric and spectroscopic models are used to determine the response functions for several types of nadir and limb sounding radiometers.     

灰色GM(1,1)模型及其在电力负荷预测中的应用

讨论了灰色模型GM(1,1)及其改进模型在电力负荷预测中的应用.从灰色理论建模特点出发,提出使用加权均值生成原始数据序列的数据生成方法,在进行平滑的非负电力负荷数据序列的预测中取得了较好的效果.通过后验差检验,对传统的灰色系统GM(1,1)模型和加权均值的GM(1,1)模型进行了比较分析.实例证明,加权均值生成数据的方法进行建模具有较好的精度,在实际电力预测系统中有很好的应用价值.     

A rapid inversion and resolution analysis of magnetic microscope data by the subtractive optimally localized averages method

Modern scanning magnetic microscopes have the potential for fine-scale magnetic investigations of rocks. Observations at high spatial resolution produce large volumes of data, and the interpretation of these data is a nontrivial task. We have developed software using an efficient magnetic inversion technique that explicitly constructs the spatially localized Backus-Gilbert averaging kernel. Our approach, using the subtractive optimally localized averages (SOLA) method (Pijpers, R.P., Thompson, M.J., 1992. Faster formulations of the optimally localized averages method for helioseismic inversions. Astronomy and Astrophysics 262, L33-L36), yield a unidirectional magnetization. The averaging kernel expresses the spatial resolution of the inversion and is valuable for paleomagnetic application of the scanning magnetic microscope. Inversion examples for numerical magnetization patterns are provided to exhibit the performance of the method. Examples of actual magnetic field data collected from thin sections of natural rocks measured with a magnetoimpedance (MI) magnetic microscope are also provided. Numerical tests suggest that the data-independent averaging kernel is desirable for a point-to-point comparison among multiple data. Contamination by vector magnetization components can be estimated by the averaging kernel. We conclude that the SOLA method is a useful technique for paleomagnetic and rock magnetic investigations using scanning magnetic microscopy.     

Nonparametric Approximation of the Density Function Logarithm of the Two-dimensional Random Variable

Consideration was given to a method for approximating the probability density of a two-dimensional random variable with separate stages of generating the local estimates and smoothing the random errors. It was proposed to decompose the space on the basis of the source data into minimal-size domains where the local estimates of the density logarithm which correspond to the observation model with additive errors accepted in the regression analysis were generated. The error covariance matrix was shown to be completely definite and independent of the original density, which made it possible to apply the apparatus of nonparametric regression to optimizing the choice of the smoothing parameter.