Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering

Background: Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. Methodology/Principal Findings: To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component. Conclusions: The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals

Denoising techniques - a comparison

Visual information transmitted in the form of digital images is becoming a major method of communication in the modern age, but the image obtained after transmission is often corrupted with noise. The received image needs processing before it can be used in applications. Image denoising involves the manipulation of the image data to produce a visually high quality image. This thesis reviews the existing denoising algorithms, such as filtering approach, wavelet based approach, and multifractal approach, and performs their comparative study. Different noise models including additive and multiplicative types are used. They include Gaussian noise, salt and pepper noise, speckle noise and Brownian noise. Selection of the denoising algorithm is application dependent. Hence, it is necessary to have knowledge about the noise present in the image so as to select the appropriate denoising algorithm. The filtering approach has been proved to be the best when the image is corrupted with salt and pepper noise. The wavelet based approach finds applications in denoising images corrupted with Gaussian noise. In the case where the noise characteristics are complex, the multifractal approach can be used. A quantitative measure of comparison is provided by the signal to noise ratio of the image

Application of Dual-Tree Complex Wavelet Transforms to Burst Detection and RF Fingerprint Classification

This work addresses various Open Systems Interconnection (OSI) Physical (PHY) layer mechanisms to extract and exploit RF waveform features (”fingerprints”) that are inherently unique to specific devices and that may be used to provide hardware specific identification (manufacturer, model, and/or serial number). This is addressed by applying a Dual-Tree Complex Wavelet Transform (DT-CWT) to improve burst detection and RF fingerprint classification. A ”Denoised VT” technique is introduced to improve performance at lower SNRs, with denoising implemented using a DT-CWT decomposition prior to Traditional VT processing. A newly developed Wavelet Domain (WD) fingerprinting technique is presented using statistical WD fingerprints with Multiple Discriminant Analysis/Maximum Likelihood (MDA/ML) classification. The statistical fingerprint features are extracted from coefficients of a DT-CWT decomposition. Relative to previous Time Domain (TD) results, the enhanced WD statistical features provide improved device classification performance. Additional performance sensitivity results are presented to demonstrate WD fingerprinting robustness for variation in burst location error, MDA/ML training and classification SNRs, and MDA/ML training and classification signal types. For all cases considered, the WD technique proved to be more robust and exhibited less sensitivity when compared with the TD Technique

Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution

Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed

Analytical formulation of the fractal dimension of filtered stochastic signals

International audienceThe aim of this study was to investigate the effects of a linear filter on the regularity of a given stochastic process in terms of the fractal dimension. This general approach, described in a continuous time domain, is new and is characterized by its simplicity. The framework of this problem is general since it emerges when a fractal process undertakes a transformation, as is the case in denoising or measurement processes