Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the Chaos Game Representation (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene-coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent sub-periods in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration.;This work examines the model\u27s behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system information dynamics correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed

Matched wavelet construction and its application to target detection

This dissertation develops a new wavelet design technique that produces a wavelet that matches a desired signal in the least squares sense. The Wavelet Transform has become very popular in signal and image processing over the last 6 years because it is a linear transform with an infinite number of possible basis functions that provides localization in both time (space) and frequency (spatial frequency). The Wavelet Transform is very similar to the matched filter problem, where the wavelet acts as a zero mean matched filter. In pattern recognition applications where the output of the Wavelet Transform is to be maximized, it is necessary to use wavelets that are specifically matched to the signal of interest. Most current wavelet design techniques, however, do not design the wavelet directly, but rather, build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a multiresolution analysis that is generated by a scaling function which has a specific corresponding wavelet. In this dissertation, an algorithm for finding both symmetric and asymmetric matched wavelets is developed. It will be shown that under certain conditions, the matched wavelets generate an orthonormal basis of the Hilbert space containing all finite energy signals. The matched orthonormal wavelets give rise to a pair of Quadrature Mirror Filters (QMF) that can be used in the fast Discrete Wavelet Transform. It will also be shown that as the conditions are relaxed, the algorithm produces dyadic wavelets which when used in the Wavelet Transform provides significant redundancy in the transform domain. Finally, this dissertation develops a shift, scale and rotation invariant technique for detecting an object in an image using the Wavelet Radon Transform (WRT) and matched wavelets. The detection algorithm consists of two levels. The first level detects the location, rotation and scale of the object, while the second level detects the fine details in the object. Each step of the wavelet matching algorithm and the object detection algorithm is demonstrated with specific examples

A quality metric to improve wrapper feature selection in multiclass subject invariant brain computer interfaces

Title from PDF of title page, viewed on June 5, 2012Dissertation advisor: Reza DerakhshaniVitaIncludes bibliographical references (p. 116-129)Thesis (Ph.D.)--School of Computing and Engineering. University of Missouri--Kansas City, 2012Brain computer interface systems based on electroencephalograph (EEG) signals have limitations which challenge their application as a practical device for general use. The signal features generated by the brain states we wish to detect possess a high degree of inter-subject and intra-subject variation. Additionally, these features usually exhibit a low variation across each of the target states. Collection of EEG signals using low resolution, non-invasive scalp electrodes further degrades the spatial resolution of these signals. The majority of brain computer interface systems to date require extensive training prior to use by each individual user. The discovery of subject invariant features could reduce or even eliminate individual training requirements. To obtain suitable subject invariant features requires search through a high dimension feature space consisting of combinations of spatial, spectral and temporal features. Poorly separable features can prevent the search from converging to a usable solution as a result of degenerate classifiers. In such instances the system must detect and compensate for degenerate classifier behavior. This dissertation presents a method to accomplish this search using a wrapper architecture comprised of a sequential forward floating search algorithm coupled with a support vector machine classifier. This is successfully achieved by the introduction of a scalar Quality (Q)-factor metric, calculated from the ratio of sensitivity to specificity of the confusion matrix. This method is successfully applied to a multiclass subject independent BCI using 10 untrained subjects performing 4 motor tasks.Introduction to brain computer interface systems -- Historical perspective and state of the art -- Experimental design -- Degeneracy in support vector machines -- Discussion of research -- Results -- Conclusion -- Appendix A. Information transfer rate -- Appendix B. Additional surface plots for individual tasks and subject

Modeling and estimation of multiresolution stochastic processes

Includes bibliographical references (p. 47-51).Caption title.Research supported in part by the National Science Foundation. ECS-8700903 Research supported in part by the Air Force Office of Scientific Research. AFOSR-88-0032 Research supported in part by the US Army Research Office. DAAL03-86-K-0171 Research supported in part by INRIA.Michele Basseville ... [et al.]