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Local and global analysis of multifractal singularity spectrum through wavelets

Local and global analysis of multifractal singularity spectr...

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Canadian Conference on electrical and computer engineering 2005

作者： Faghfouri, A. Kinsner, W. Dept. of Electrical and Computer Engineering Signal and Data Compression Laboratory University of Manitoba Winnipeg Man. R3T 5V6 Canada

This paper presents the implementation aspects pertinent to the computation of the multifractal singularity spectrum through wavelets, and the methods of overcoming them. Multifractals are mixtures of monofractals, and monofractals are self-affine objects that hold power law relationships over several scales. Such multifractals can be detected and measured through a singularity spectrum. Many natural and artificial phenomena such as turbulence, diffusion limited aggregates, and electrical discharges exhibit multifractality. Since these phenomena are highly nonlinear and nonstationary, regular analyses such as Fourier decomposition cannot characterize them effectively. In order to characterize, compare and quantify multifractal objects, appropriate measures such as the Rényi fractal dimension spectrum (RS) and Mandelbrot singularity spectrum (MS) are required. There are two major methods for calculating a singularity spectrum;one is through Legendre transform of the RS, and the other is through the wavelet transform modulus maxima (WTMM) method. This paper provides solutions to the difficulties that arise in the computation of the MS through WTMM, for one-dimensional signals and compares them to the existing multifractal literature and software implementations. Appropriate mother wavelets, continuous wavelet implementation, and thresholding of the wavelet coefficients are also discussed. © 2005 IEEE.

关键词： signal processing

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Surrogate ECG signals for the null-hypothesis analysis of heart monitoring

Surrogate ECG signals for the null-hypothesis analysis of he...

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Canadian Conference on electrical and computer engineering (CCECE)

作者： M. Potter W. Kinsner Department of Electrical and Computer Engineering Signal and Data Compression Laboratory University of Manitoba Winnipeg MAN Canada

This paper introduces a class of synthetic electrocardiograms (ECG) for the purpose of testing the sensitivity and robustness of heart-monitoring techniques in controlled and reproducible simulations. These ECG surrogates are constructed by adapting an existing standard ECG synthesizer to act as a modulator on a tachogram input, enabling null-hypothesis analysis on heart-rate variability. This establishes an empirical link between the tachogram literature and the design of heart monitoring techniques. The new methodology is demonstrated experimentally and its performance is discussed

关键词： Electrocardiography signal analysis Heart

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compression of multifractal object boundaries: a comparison of two approaches

Compression of multifractal object boundaries: a comparison ...

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Canadian Conference on electrical and computer engineering (CCECE)

作者： S. Siddiqui A. El-Boustani W. Kinsner Signal and Data Compression Laboratory Department of Electrical and Computer Engineering University of Manitoba Winnipeg MAN Canada

This paper presents a comparative study of two approaches that address the problem of compression of arbitrary object boundaries resulting from image segmentation. The first approach uses multiresolution based techniques, in which the boundary is represented compactly by two sets of descriptors and control points which are obtained by applying wavelet and fractal analysis. The midpoint displacement algorithm is then applied to the two sets of control points in order to reconstruct the boundaries with the required fractal dimension. The second approach is based on the iterated function system (IFS). In this approach, the object boundary is regarded as an attractor of an IFS having the same Renyi fractal dimension spectrum as the original boundary. The experimental results show that the multifractal object boundaries can be modelled compactly using both approaches. The compression ratio achieved for the wavelet-based approach was 285:1, while for the IFS-based approach it was 52:1. These results can be compared with state of the art image compression techniques such as JPEG2000

关键词： Fractals Image coding Image segmentation Transform coding Video compression Shape Curve fitting Data compression Laboratories signal resolution

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Local and global analysis of multifractal singularity spectrum through wavelets

Local and global analysis of multifractal singularity spectr...

引用

Canadian Conference on electrical and computer engineering (CCECE)

作者： A. Faghfouri W. Kinsner Department of Electrical and Computer Engineering Signal and Data Compression Laboratory University of Manitoba Winnipeg MAN Canada

This paper presents the implementation aspects pertinent to the computation of the multifractal singularity spectrum through wavelets, and the methods of overcoming them. Multifractals are mixtures of monofractals, and monofractals are self-affine objects that hold power law relationships over several scales. Such multifractals can be detected and measured through a singularity spectrum. Many natural and artificial phenomena such as turbulence, diffusion limited aggregates, and electrical discharges exhibit multifractality. Since these phenomena are highly nonlinear and nonstationary, regular analyses such as Fourier decomposition cannot characterize them effectively. In order to characterize, compare and quantify multifractal objects, appropriate measures such as the Renyi fractal dimension spectrum (RS) and Mandelbrot singularity spectrum (MS) are required. There are two major methods for calculating a singularity spectrum; one is through Legendre transform of the RS, and the other is through the wavelet transform modulus maxima (WTMM) method. This paper provides solutions to the difficulties that arise in the computation of the MS through WTMM, for one-dimensional signals and compares them to the existing multifractal literature and software implementations. Appropriate mother wavelets, continuous wavelet implementation, and thresholding of the wavelet coefficients are also discussed

关键词： Fractals Wavelet analysis Continuous wavelet transforms Wavelet transforms Equations Data engineering Data compression Laboratories Power engineering computing Aggregates

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Rotation sensitivity of independent component analysis to outliers

Rotation sensitivity of independent component analysis to ou...

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Canadian Conference on electrical and computer engineering (CCECE)

作者： N. Gadhok W. Kinsner Department of Electrical and Computer Engineering Signal and Data Compression Laboratory University of Manitoba Winnipeg MAN Canada

This paper evaluates the outlier sensitivity of five independent component analysis (ICA) algorithms (FastICA, extended-infomax, JADE, radical-ICA, and beta-divergence) using (i) the Amari separation performance index, (ii) the optimum angle of rotation error, and (iii) the contrast function difference, in an outlier-contaminated mixture simulation. The Amari separation performance index has revealed a strong sensitivity of JADE and FastICA (using 3rd- and 4th-order nonlinearities) to outliers. However, the two contrast measures demonstrated conclusively that beta-divergence is the least outlier-sensitive algorithm, followed by radical-ICA, FastICA (exponential and hyperbolic-tangent nonlinearities), extended-infomax, JADE, and FastICA (3rdand 4th-order nonlinearities) in an outlier-contaminated mixture of two uniformly distributed signals. The novelty of this paper is the development of an unbiased optimization-landscape environment for assessing outlier sensitivity, as well as the optimum angle of rotation error and the contrast function difference as promising new measures for assessing the outlier sensitivity of ICA algorithms

关键词： Independent component analysis signal processing algorithms Higher order statistics Statistical analysis Robustness Performance analysis Pollution measurement Rotation measurement Source separation Data compression

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Robust independent component analysis for cognitive informatics

Robust independent component analysis for cognitive informat...

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IEEE International Conference on Cognitive Informatics

作者： N. Gadhok W. Kinsner Department of Electrical and Computer Engineering Signal and Data Compression Laboratory University of Manitoba Winnipeg MAN Canada

This paper evaluates the outlier sensitivity of five independent component analysis (ICA) algorithms (FastICA, extended-Infomax, JADE, radical, and /spl beta/-divergence) using: (i) the Amari separation performance index, (ii) the optimum angle of rotation error, and (iii) the contrast function difference, in an outlier-contaminated mixture simulation. The Amari separation performance index has revealed a strong sensitivity of JADE and FastICA, using 3rd- and 4th- order nonlinearities, to outliers. However, the two contrast measures demonstrated conclusively that /spl beta/-divergence is the least outlier-sensitive algorithm, followed by Radical, FastICA (exponential and hyperbolic-tangent nonlinearities), extended-Infomax, JADE, and FastICA (3rd-and 4th-order nonlinearities) in an outlier-contaminated mixture of two uniformly distributed signals. The novelty of this paper is the development of an unbiased optimization-landscape environment for assessing outlier sensitivity, as well as the optimum angle of rotation error and the contrast function difference as promising new measures for assessing the outlier sensitivity of ICA algorithms.

关键词： Robustness Independent component analysis Cognitive informatics Electroencephalography signal processing algorithms Statistical analysis Performance analysis Brain modeling Biomedical measurements Pollution measurement

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A unified approach to fractal dimensions

A unified approach to fractal dimensions

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IEEE International Conference on Cognitive Informatics

作者： W. Kinsner Signal and Data Compression Laboratory Department of Electrical and Computer Engineering University of Manitoba Winnipeg MAN Canada

Many scientific papers treat the diversity of fractal dimensions as mere variations on either the same theme or a single definition. There is a need for a unified approach to fractal dimensions for there are fundamental differences between their definitions. This paper presents a new description of three essential classes of fractal dimensions based on: (i) morphology, (ii) entropy, and (iii) transforms, all unified through the generalized entropy-based Renyi fractal dimension spectrum. It discusses practical algorithms for computing 15 different fractal dimensions representing the classes. Although the individual dimensions have already been described in the literature, the unified approach presented in this paper is unique in terms of (i) its progressive development of the fractal dimension concept, (ii) similarity in the definitions and expressions, (iii) analysis of the relation between the dimensions, and (iv) their taxonomy. As a result, a number of new observations have been made, and new applications discovered. Of particular interest are behavioural processes such as dishabituation, irreversible and birth-death growth phenomena e.g., diffusion-limited aggregates, DLAs, dielectric discharges, and cellular automata, as well as dynamical nonstationary transient processes such as speech and transients in radio transmitters, multifractal optimization of image compression using learned vector quantization with Kohonen 's self-organizing feature maps (SOFMs), and multifractal-based signal denoising.

关键词： Fractals Morphology Entropy Taxonomy Aggregates Dielectrics Speech processing Radio transmitters Image coding Vector quantization

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Platform-independent implementation of 3D-sound computer interface icons for subjects with visual impairments

Platform-independent implementation of 3D-sound computer int...

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9th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2005

作者： Faller II, Kenneth John Prendes, Joaquin Barreto, Armando Digital Signal Processing Laboratory Electrical and Computer Engineering Department Florida International University Miami FL 33174 United States

ISBN: (纸本)9806560531

This paper describes a platform-independent system which adds spatial auditory feedback to the icons of a computer interface in order to assist visually impaired individuals during icon location and selection. In this enhanced system, icons have 3D sound properties, in addition to their graphical properties. Each icon has a specific sound associated with it. As the cursor is moved throughout the interface, the user is able to hear, spatially, in which direction and at what distance each icon is located, with respect to the cursor.

关键词： Human computer interaction

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A comparison of image quality metric performances under practical conditions

A comparison of image quality metric performances under prac...

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IEEE International Conference on Image Processing 2005, ICIP 2005

作者： De Freitas Zampolo, Ronaldo Seara, Rui LaPS - Signal Processing Laboratory Department of Electrical and Computer Engineering Federal University of Pará 66075-110 Belém PA Brazil LINSE - Circuits and Signal Processing Laboratory Department of Electrical Engineering Federal University of Santa Catarina 88040-900 Florianópolis SC Brazil

ISBN: (纸本)0780391349

In this paper three image quality metrics are compared: mean-square error (MSB), noise quality measure (NQM), and structural information metric (SIM). Such a comparison is made in order to evaluate the performance of those different metrics under practical conditions. Experimental results along with statistical indices of performance are provided. The referred results suggest that there are situations in which the MSB-based metric outperforms the two other considered metrics. © 2005 IEEE.

关键词： Image quality

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Mixed PCA/ICA spectral/spatial compression for hyperspectral imagery

Mixed PCA/ICA spectral/spatial compression for hyperspectral...

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Chemical and Biological Standoff Detection III

作者： Wang, Jing Chang, Chein-I. Remote Sensing Signal and Image Processing Laboratory Department of Computer Science and Electrical Engineering University of Maryland Baltimore County Baltimore MD 21250

Principal components analysis (PCA) has been widely used in many applications, particularly, data compression. Independent component analysis (ICA) has been also developed for blind source separation along with many other applications such as channel equalization, speech processing. Recently, it has been shown that the ICA can be also used for hyperspectral data compression. This paper investigates these two transforms in hyperspectral data compression and further evaluates their strengths and weaknesses in applications of target detection, mixed pixel classification and abundance quantification. In order to take advantage of the strengths of both transform, a new transform, called mixed PCA/ICA transform is developed in this paper. The idea of the proposed mixed PCA/ICA transform is derived from the fact that it can integrate different levels of information captured by the PCA and ICA. In doing so, it combines m principal components (PCs) resulting from the PCA and n independent components (ICs) generated by the ICA to form a new set of (m+n) mixed components used for hyperspectral data compression. The resulting transform is referred to as mixed (m,n)-PCA/ICA transform. In order to determine the total number of components, p needed to be generated for the mixed (m,m)-PCA/ICA transform, a recently developed virtual dimensionality (VD) is introduced to estimate the p where p = m + n. If m = p and n = 0, then mixed (m,n)-PCA/ICA transform is reduced to PCA transform. On the other hand, if m = 0 and n = p, then mixed (m,n)-PCA/ICA transform is reduced to ICA. Since various combinations of m and n have different impacts on the performance of the mixed PCA/ICA spectral/spatial compression in applications, experiments based on subpixel detection and mixed pixel quantification are conducted for performance evaluation.

关键词： Image compression

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