Spectral analysis for nonstationary audio

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This paper provides theoretical analysis of the approximations, and introduces JEFAS, a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.Comment: IEEE/ACM Transactions on Audio, Speech and Language Processing, Institute of Electrical and Electronics Engineers, In pres

Tomographic inversion using ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accepted dates). Corrected typ

A Neutral Network Based Vehicle Classification System for Pervasive Smart Road Security

Pervasive smart computing environments make people get accustomed to convenient and secure services. The overall goal of this research is to classify vehicles along the I215 freeway in Salt Lake City, USA. This information will be used to predict future roadway needs and the expected life of a roadway. The classification of vehicles will be performed by a synthesis of multiple sets of features. All feature sets have not yet been determined; however, one such set will be the reduced wavelet transform of the image of a vehicle. In order to use such a feature, it is necessary that the image be normalized with respect to size, position, and so on. For example, a car in the right most lane in an image will appear smaller than one in the left most lane, because the right most lane is closest to the camera. Likewise, a vehicle’s size will vary depending on where in a lane its image is captured. In our case, the image capture area for each lane is approximately 100 feet of roadway. A goal of this paper is to normalize the image of a vehicle so that regardless of its lane or position in a lane, the features will be approximately the same. The wavelet transform itself will not be used directly for recognition. Instead, it will be input to a neural network and the output of the neural network will be one element of the feature set used for recognition

Multilevel functional principal component analysis

The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilevel functional principal component analysis (MFPCA), a novel statistical methodology designed to extract core intra- and inter-subject geometric components of multilevel functional data. Though motivated by the SHHS, the proposed methodology is generally applicable, with potential relevance to many modern scientific studies of hierarchical or longitudinal functional outcomes. Notably, using MFPCA, we identify and quantify associations between EEG activity during sleep and adverse cardiovascular outcomes.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS206 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Natural variation in Drosophila melanogaster

This work is dedicated to studying natural variation in D. melanogaster at the DNA sequence and gene expression level. In addition I present a new version of the DNA polymorphism analysis program VariScan, which includes significant improvements. In CHAPTER 1 I describe a genome scan of single nucleotide polymorphism in two natural D. melanogaster populations (from Africa and Europe) on the third chromosome. Together with polymorphism data previously published for the X chromosome of the same populations, this allows a comparative study of the polymorphism patterns of the X chromosome and an autosome. The frequency spectrum of mutations and the patterns of linkage disequilibrium are investigated. The observed patterns indicate that there is a significant difference in the behavior of the two chromosomes, as has already been suggested by previous studies. To uncover the reasons for this a coalescent based maximum likelihood method is applied that incorporates the effects of demographic history and unequal sex ratios. For the African population the differential behavior of the chromosomes can be explained by its demographic history and an excess of females. In Europe, a population bottleneck and an excess of males alone cannot explain the patterns we observe. The additional action of positive selection in this population is proposed as a possible explanation. In CHAPTER 2 I investigate the variation in gene expression of the two aforementioned populations. Whole-genome microarrays are used to study levels of expression for 88% of all known genes in eight adult males from both populations. The observed levels of expression variation are equal in Africa and Europe, despite the fact that DNA sequence variation is much higher in Africa. This is evidence for the action of stabilizing selection governing levels of expression polymorphism. Supporting this view, genes involved in many different functions, and are therefore on strong selective constraint, show less variation than do genes with only few functions. The experimental design allows the search for genes which differ in their expression patterns between Europe and Africa and might therefore have undergone adaptive evolution. Detected candidates include genes putatively involved in insecticide resistance and food choice. Surprisingly, many genes over-expressed in Africa are involved in the formation and function of the flying apparatus. In CHAPTER 3 I present version 2 of the program VariScan. This program was designed to analyse patterns of DNA sequence polymorphism on a chromosomal scale. The functionality of the core analysis tool, the wavelet decomposition, is described. In addition, multiple improvements to the previous version are presented. The program now supports the “pairwise deletion” option. This is essential for analysing data at the chromosome scale, since such data often contains incomplete information. It is now possible to add outgroup information, which allows the calculation of additional statistics. Furthermore, the separate analysis of different predefined chromosomal regions is added as an option. To increase the user friendliness, a graphical user interface is now included as part of the software package. Finally, VariScan is applied to published and computer-generated data and the ability of the wavelet-based analysis to uncover chromosomal regions with interesting DNA polymorphism patterns is demonstrated

Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases

We investigate the optimality for model selection of the so-called slope heuristics, $V$-fold cross-validation and $V$-fold penalization in a heteroscedastic with random design regression context. We consider a new class of linear models that we call strongly localized bases and that generalize histograms, piecewise polynomials and compactly supported wavelets. We derive sharp oracle inequalities that prove the asymptotic optimality of the slope heuristics---when the optimal penalty shape is known---and $V$ -fold penalization. Furthermore, $V$-fold cross-validation seems to be suboptimal for a fixed value of $V$ since it recovers asymptotically the oracle learned from a sample size equal to $1-V^{-1}$ of the original amount of data. Our results are based on genuine concentration inequalities for the true and empirical excess risks that are of independent interest. We show in our experiments the good behavior of the slope heuristics for the selection of linear wavelet models. Furthermore, $V$-fold cross-validation and $V$-fold penalization have comparable efficiency