Signal smoothness estimation in hölder spaces

Previous research has shown that wavelet method can be used to estimate the Besov smoothness of a function (signal). This paper describes an algorithm that is based on the magnitudes of the wavelet coefficients and linear regression model to estimate the smoothness of different signals of one and two-dimensional in the Hölder spaces. Computational results show that the Holder smoothness of the general two-dimensional image is between 0.2 and 0.7. We compare our results with those in Besov smoothness spaces and discuss the smoothness relations between these two function spaces.     

Compactly Supported Biorthogonal Wavelet Bases on the Body Centered Cubic Lattice

In this work, we present a family of compact, biorthogonal wavelet filter banks that are applicable to the Body Centered Cubic (BCC) lattice. While the BCC lattice has been shown to have superior approximation properties for volumetric data when compared to the Cartesian Cubic (CC) lattice, there has been little work in the way of designing wavelet filter banks that respect the geometry of the BCC lattice. Since wavelets have applications in signal de‐noising, compression, and sparse signal reconstruction, these filter banks are an important tool that addresses some of the scalability concerns presented by the BCC lattice. We use these filters in the context of volumetric data compression and reconstruction and qualitatively evaluate our results by rendering images of isosurfaces from compressed data.     

基于神经网络的小波分析在两相流不稳定性中的应用

小波变换和分解具有良好的时频局部化特性,使得小波分析被广泛地应用于时频分析中。本文结合了神经网络良好的自学习和自适应能力,得到小波神经网络,通过计算机仿真实现了对两相流不稳定性的辨识。     

On the regularization of dynamic data reconciliation problems

Dynamic data reconciliation problems are discussed from the perspective of the mathematical theory of ill-posed inverse problems. Regularization is of crucial importance to obtain satisfactory estimation quality of the reconciled variables. Usually, some penalty is added to the least-squares objective to achieve a well-posed problem. However, appropriate discretization schemes of the time-continuous problem act themselves as regularization, reducing the need of problem modification. Based on this property, we suggest to refine successively the discretization of the continuous problem starting from a coarse grid, to find a suitable regularization which renders a good compromise between (measurement) data and regularization error in the estimate. In particular, our experience supports the conjecture, that non-equidistant discretization grids offer advantages over uniform grids.     

Robust multi-scale principal components analysis with applications to process monitoring

Robust multi-scale principal component analysis (RMSPCA) improves multi-scale principal components analysis (MSPCA) techniques by incorporating the uncertainty of signal noise distributions and eliminating/down-weighting the effects of abnormal data in the training set. The novelty of the approach is to integrate MSPCA with the robustness to the typical normality assumption of noisy data. By using an M-estimator based on the generalized T distribution, RMSPCA adaptively transforms the data in the score space at each scale in order to eliminate/down-weight the effects of the outliers in the original data. The robust estimation of the covariance or correlation matrix at each scale is obtained by the proposed approach so that accurate MSPCA models can be obtained for process monitoring purposes. The performance of the proposed approach in process fault detection is illustrated and compared with that of the conventional MSPCA approach through a pilot-scale setting.     

Optical character recognition of the Orthodox Hellenic Byzantine Music notation

In this paper we present for the first time, the development of a new system for the off-line optical recognition of the characters used in the orthodox Hellenic Byzantine Music notation, that has been established since 1814. We describe the structure of the new system and propose algorithms for the recognition of the 71 distinct character classes, based on Wavelets, 4-projections and other structural and statistical features. Using a nearest neighbor classifier, combined with a post classification schema and a tree-structured classification philosophy, an accuracy of 99.4% was achieved, in a database of about 18,000 Byzantine character patterns that have been developed for the needs of the system.     

Wavelet-based analysis of multiscale phenomena: application to material porosity and identification of dominant scales

The paper presents a general process that utilizes wavelet analysis in order to link information on material properties at several scales. In the particular application addressed analytically and numerically, multiscale porosity is the source of material structure or heterogeneity, and the wavelet-based analysis of multiscale information shows clearly its role on properties such as resistance to mechanical failure. Furthermore, through the statistical properties of the heterogeneity at a hierarchy of scales, the process clearly identifies a dominant scale or range of scales. Special attention is paid to porosity appearing at two distinct scales far apart from each other since this demonstrates the process in a lucid fashion. Finally, the paper suggests ways to extend the process to general multiscale phenomena, including time scaling.     

Extraction of wave characteristics from wavelet-based spectral finite element formulation

In this paper, a spectrally formulated wavelet finite element is developed and is used not only to study wave propagation in 1-D waveguides but also to extract the wave characteristics, namely the spectrum and dispersion relation for these waveguides. The use of compactly supported Daubechies wavelet basis circumvents several drawbacks of conventional FFT-based Spectral Finite Element Method (FSFEM) due to the required assumption of periodicity, particularly for time domain analysis. In this work, a study is done to use the formulated Wavelet-based Spectral Finite Element (WSFE) directly for such frequency domain analysis. This study shows that in WSFE formulation, a constraint on the time sampling rate is paced to avoid spurious dispersion being introduced in the analysis. Numerical experiments are performed to study frequency-dependent wave characteristics (dispersion and spectrum relations) in elementary rod, Euler–Bernoulli and Timoshenko beams. The effect of sampling rate on the accuracy of WSFE solution for both impulse and modulated sinusoidal loading with different frequency content is shown through different examples. In all above cases, comparison with FSFEM are provided to highlight the advantages and limitations of WSFE.     

Using fractal image analysis to characterize microstructure of low-fat stirred yoghurt manufactured with microparticulated whey protein

Differences in the microstructure of low fat yoghurt manufactured with microparticulated whey proteins used as fat replacer were investigated. Images were obtained by confocal laser scanning microscopy and studied using a technique for image analysis that combines an initial 2D-wavelet compression followed by fractal analysis and inspection of the fractal curves by principal components analysis (PCA). One commercial and three experimental microparticulated ingredients with different chemical characteristics were used in the yoghurt formulations and compared to both full and low fat yoghurts without fat replacer. The results showed that the amount of native and soluble whey proteins present in the microparticles had a positive influence on the structure of the formed gel. The created structure, dominated by dense aggregates and low amount of serum, had an increased degree of self similarity or fractality with yoghurts in which fat was present.