General Nonlinear Transformation Research Articles

Extended noise equalisation for image compression in microscopical applications

Abstract Today’s camera systems used for machine vision and scientific applications have intra-scene dynamic ranges up to 16 bit and therefore A/D converters with up to 16 bit resolution per pixel. Unfortunately, the linear amplification of electrons also forces a linear or even quadratic increase of the image noise variance with the signal. Based on a method published in 2016 (B. Jähne, M. Schwarzbauer, tm-Technisches Messen 83.1), this paper describes a more general nonlinear transformation which equalizes the combined effect of temporal noise and photo-response non-uniformity (PRNU) and/or temporal noise in the illumination system of an image sensor. With this generalisation it is possible to use the equalisation also for microscopic applications for which an example is discussed.

Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation

The geometries of many problems of practical interest are created from circular or elliptic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations (BIEs) and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular properties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occurring in the boundary element method (BEM) for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

BEM analysis of thin structures for thermoelastic problems

A new boundary element method is developed for solving thin-body thermoelastic problems in this paper. Firstly, the novel regularized boundary integral equations (BIEs) containing indirect unknowns are proposed to cancel the singularity of fundamental solutions. Secondly, a general nonlinear transformation available for high-order geometry elements is introduced in order to remove or damp out the near singularity of fundamental solutions, which is crucial for accurate solutions of thin-body problems. Finally, the domain integrals arising in both displacement and its derivative integral equations, caused by the thermal loads, are regularized using a semi-analytical technique. Six benchmark examples are examined. Results indicate that the proposed method is accurate, convergent and computationally efficient. The proposed method is a competitive alternative to existing methods for solving thin-walled thermoelastic problems.

Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Ly-α forest

On large scales a nonlinear transformation of matter density field can be viewed as a biased tracer of the density field itself. A nonlinear transformation also modifies the redshift space distortions in the same limit, giving rise to a velocity bias. In models with primordial nongaussianity a nonlinear transformation generates a scale dependent bias on large scales. We derive analytic expressions for the large scale bias,the velocity bias and the redshift space distortion (RSD) parameter β, as well as the scale dependent biasfrom primordial nongaussianity for a general nonlinear transformation. These biases can be expressed entirely in terms of the one point distribution function (PDF) of the final field and the parameters of the transformation. The analysis shows that one can view the large scale bias different from unity and primordial nongaussianity bias as a consequence of converting higher order correlations in densityinto 2-point correlations of its nonlinear transform. Our analysis allows one to devise nonlinear transformations with nearly arbitrary bias properties, which can be used to increase the signal in the large scale clustering limit. We apply the results to the ionizing equilibrium model of Lyman-α forest, in which Lyman-α flux F is related to the density perturbation δ via a nonlinear transformation. Velocity bias can be expressed as an average over the Lyman-α flux PDF. At z = 2.4 we predict the velocity bias of -0.1, compared to the observed value of −0.13±0.03. Bias and primordial nongaussianity bias depend on the parameters of the transformation. Measurements of bias can thus be used to constrain these parameters, and for reasonable values of the ionizing background intensity we can match the predictions to observations. Matching to the observed values we predict the ratio of primordial nongaussianity bias to bias to have the opposite sign and lower magnitude than the corresponding values for the highly biased galaxies, but this depends on the model parameters and can also vanish or change the sign.

A non-linear transformation applied to boundary layer effect and thin-body effect in BEM for 2D potential problems

The accurate numerical evaluation of nearly singular integrals plays an important role in many engineering applications. In general, these include evaluating the solution near the boundary or treating problems with thin domains, which are respectively named the boundary layer effect and the thin-body effect in the boundary element method. Although many methods of evaluating nearly singular integrals have been developed in recent years with varying degrees of success, questions still remain. In this article, a general non-linear transformation for evaluating nearly singular integrals over curved two-dimensional (2D) boundary elements is employed and applied to treat boundary layer effect and thin-body effect occurring in 2D potential problems. The introduced transformation can remove or damp out the rapid variations of nearly singular kernels and extremely high accuracy of numerical results can be achieved without increasing other computational efforts. Extensive numerical experiments indicate that the proposed transformation will be more efficient, in terms of the necessary integration points and central processing unit-time, compared to previous transformation methods, especially for dealing with thin-body problems.

BOUNDARY ELEMENT ANALYSIS OF THIN STRUCTURAL PROBLEMS IN 2D ELASTOSTATICS

Thin structures, such as thin films and coatings, have been widely designed and utilized in many industries recently. However, the widespread experimental research in thin structural problems underlies a general lack of modeling efforts which can accurately and efficiently predict their performance. In this paper, the boundary element method (BEM) based on elasticity theory is developed for two-dimensional (2D) thin structures with the thickness to length ratio in the micro (10^(-6)) or nano (10^(-9)) scales. The BEM-based approach proposed in this paper is constructed using a combination of the regularized indirect boundary integral equations (BIEs) and a general nonlinear transformation which can eliminate the nearly singular properties of the integral kernels. For the test problems studied, very promising results are obtained when the thickness to length ratio is in the orders between 10^(-6) and 10^(-9), which is sufficient for modeling most thin structures in the micro- or nano-scales.

Internal stress analysis for single and multilayered coating systems using the boundary element method

Various thin-coating films are designed and utilized for industrial applications to improve machining performance due to better temperature and wear resistant properties than their substrate counterparts. However, the widespread experimental research on thin coatings underlies a general lack of modeling efforts, which can accurately and efficiently predict the coating and thin film performance. In this paper, the boundary element method (BEM) for 2D elastostatic problems is studied for the analysis of single and multilayered coating systems. The nearly singular integrals, which is the primary obstacle associated with the BEM formulations, are dealt efficiently by using a general nonlinear transformation technique. For the test problems studied, very promising results are obtained when the thickness of coated layers is in the orders of 1.0E−6 to 1.0E−9, which is sufficient for modeling most coated systems in the micro- or nano-scales.

Maximum-Likelihood Nonlinear Transformation for Acoustic Adaptation

In this paper, we describe an adaptation method for speech recognition systems that is based on a nonlinear transformation of the feature space. In contrast to most existing adaptation methods which assume some form of affine transformation of either the feature vectors or the acoustic models that model the feature vectors, our proposed method composes a general nonlinear transformation from two transformations, one of these being an affine transformation that combines the dimensions of the original feature space, and the other being a nonlinear transformation that is applied independently to each dimension of the previously transformed feature space leading to a general multidimensional nonlinear transformation of the original feature space. This method also differs from other affine techniques in the way the parameters of the transform are shared. In most previous methods, the parameters of the transformation are shared on the basis of the phonetic class, in our method, the parameters of the nonlinear transformation are shared not on the basis of the phonetic class, but rather on the location in the feature space. Experimental results show that the method outperforms affine methods providing up to a 25% relative improvement in the word error rate in an in-car speech recognition task.

Approximately independent factors of speech using nonlinear symplectic transformation

This paper addresses the problem of representing the speech signal using a set of features that are approximately statistically independent. This statistical independence simplifies building probabilistic models based on these features that can be used in applications like speech recognition. Since there is no evidence that the speech signal is a linear combination of separate factors or sources, we use a more general nonlinear transformation of the speech signal to achieve our approximately statistically independent feature set. We choose the transformation to be symplectic to maximize the likelihood of the generated feature set. In this paper, we describe applying this nonlinear transformation to the speech time-domain data directly and to the Mel-frequency cepstrum coefficients (MFCC). We discuss also experiments in which the generated feature set is transformed into a more compact set using a maximum mutual information linear transformation. This linear transformation is used to generate the acoustic features that represent the distinctions among the phonemes. The features resulted from this transformation are used in phoneme recognition experiments. The best results achieved show about 2% improvement in recognition accuracy compared to results based on MFCC features.

98/02179 Probabilistic ranking of large scale transmission projects

A neural network learning paradigm based on information theory is proposed as a way to perform, in an unsupervised fashion, redundancy reduction among the elements of the output layer without loss of information from the sensory input. The model developed performs nonlinear decorrelation up to higher orders of the cumulant tensors and results in probabilistically independent components of the output layer. This means that we don't need to assume Gaussian distribution at either the input or the output. The theory presented is related to the unsupervised learning theory of Barlow, which proposes redundancy reduction as the goal of cognition. When nonlinear units are used (sigmoid or higher-order pi-neurons), nonlinear principal component analysis is obtained. In this case, nonlinear manifolds can be reduced to minimum dimension manifolds. If such units are used the network performs a generalized principal component analysis in the sense that non-Gaussian distributions can be linearly decorrelated and higher orders of the correlation tensors are also taken into account. The basic structure of the architecture involves a general transformation that is volume conserving and therefore the entropy, yielding a map without loss of information. Minimization of the mutual information among the output neurons eliminates the redundancy between the outputs and results in statistical decorrelation of the extracted features. This is known as factorial learning. To sum up, this paper presents a model of factorial learning for general nonlinear transformations of an arbitrary non-Gaussian (or Gaussian) environment with statistically nonlinearly correlated input. Simulations demonstrate the effectiveness of this method.

Local Equilibrium Assumption for Ordering Dynamics

The local equilibrium assumption and the general nonlinear transformation of the order parameter in the phase ordering dynamics are discussed. By this method we can relate the kinetic equation similar to that of Kawasaki, Yalabic and Gunton (KYG) with that of Ohta, Jasnow and Kawasaki (OJK). The discussion is done both for the scalor and vector field order parameter.

Nonlinear higher-order statistical decorrelation by volume-conserving neural architectures

A neural network learning paradigm based on information theory is proposed as a way to perform, in an unsupervised fashion, redundancy reduction among the elements of the output layer without loss of information from the sensory input. The model developed performs nonlinear decorrelation up to higher orders of the cumulant tensors and results in probabilistically independent components of the output layer. This means that we don't need to assume Gaussian distribution at either the input or the output. The theory presented is related to the unsupervised learning theory of Barlow, which proposes redundancy reduction as the goal of cognition. When nonlinear units are used (sigmoid or higher-order pi-neurons), nonlinear principal component analysis is obtained. In this case, nonlinear manifolds can be reduced to minimum dimension manifolds. If such units are used the network performs a generalized principal component analysis in the sense that non-Gaussian distributions can be linearly decorrelated and higher orders of the correlation tensors are also taken into account. The basic structure of the architecture involves a general transformation that is volume conserving and therefore the entropy, yielding a map without loss of information. Minimization of the mutual information among the output neurons eliminates the redundancy between the outputs and results in statistical decorrelation of the extracted features. This is known as factorial learning. To sum up, this paper presents a model of factorial learning for general nonlinear transformations of an arbitrary non-Gaussian (or Gaussian) environment with statistically nonlinearly correlated input. Simulations demonstrate the effectiveness of this method.