The quality and intelligibility of single channel speech degraded by additive noise remains a challenging problem when only the noisy speech is available. An accurate estimation of the noise spectrum is important for the effective performance of speech enhancement algorithms, especially in nonstationary noise environments. This thesis addresses both two issues. First, a speech enhancement algorithm using harmonic features is introduced. A spectral weighting function is derived by constrained optimization to suppress noise in the frequency domain. Two design parameters are included in the suppression gain, namely the frequency-dependent noise-flooring parameter (FDNFP) and the gain factor. The FDNFP controls the level of admissible residual noise in the enhanced speech, while further enhancement is achieved by adaptive comb filtering using the gain factor with a peak-picking algorithm. Second, a noise estimation algorithm is proposed for nonstationary noise conditions. The speech presence probability is updated by introducing a time-frequency dependent threshold. The frequency dependent smoothing factor for noise estimation is computed based on the estimated speech presence probability in each frequency bin. This algorithm adapts quickly to nonstationary noise environments and preserves more information on weak speech phoneme. The performance of the proposed speech enhancement algorithm is evaluated in terms of Perceptual Evaluation of Speech Quality (ITU-PESQ) scores and Modified Bark Spectral Distortion (MBSD) measures, composite objective measures and listening tests. Our listening tests indicate that 16 listeners on average preferred our harmonic enhanced speech over any of three other approaches about 73% of the time. The performance of the proposed noise estimation algorithm combined with the proposed speech enhancement method in nonstionary noise environments is also tested in terms of ITU-PESQ scores and MBSD measures. Experimental results indicate that the proposed noise estimation algorithm when integrated with the harmonic enhancement method outperforms spectral subtraction, signal subspace method, a perceptually-based enhancement method with a constant noise-flooring parameter, and our original harmonic speech enhancement method in highly nonstationary noise environments.

This paper examines the time lag between the peak in the arrival rate and the peaks in the mean and variance for the number of customers in an M(t)/M(t)/1l system. We establish a necessary condition for the time at which the peak in the mean is achieved. In cases in which system utilization exceeds one during some period, we show that the peak in the mean occurs after the end of this period. / Revised October 1994

This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the Wold-Cram'er evolutionary spectrum, which is a time-dependent analogue of the spectrum of a stationary process. Existing estimators of the Wold-Cram'er evolutionary spectrum suffer from several problems, including bias in boundary regions of the time-frequency plane, poor frequency resolution, and an inability to handle the presence of purely harmonic frequencies. We propose techniques to handle all three of these problems. We propose a new estimator of the Wold-Cram'er evolutionary spectrum (the BCMTFSE) which mitigates the first problem. Our estimator is based on an extrapolation of the Wold-Cram'er evolutionary spectrum in time, using an estimate of its time derivative. We apply our estimator to a set of simulated nonstationary processes with known Wold-Cram'er evolutionary spectra to demonstrate its performance. We also propose an estimator of the Wold-Cram'er evolutionary spectrum, valid for uniformly modulated processes (UMPs). This estimator mitigates the second problem, by exploiting the structure of UMPs to improve the frequency resolution of the BCMTFSE. We apply this estimator to a simulated UMP with known Wold-Cram'er evolutionary spectrum. To deal with the third problem, one can detect and remove purely harmonic frequencies before applying the BCMTFSE. Doing so requires a consideration of the aliasing problem. We propose a frequency-domain technique to detect and unalias aliased frequencies in bivariate time series, based on the observation that aliasing manifests as nonlinearity in the phase of the complex coherency between a stationary process and a time-delayed version of itself. To illustrate this ``unaliasing'' technique, we apply it to simulated data and a real-world example of solar noon flux data. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-05 10:18:13.476

Yes / Data streams have arisen as a relevant research topic during the past decade. They are real‐time, incremental in nature, temporally ordered, massive, contain outliers, and the objects in a data stream may evolve over time (concept drift). Clustering is often one of the earliest and most important steps in the streaming data analysis workflow. A comprehensive literature is available about stream data clustering; however, less attention is devoted to the fuzzy clustering approach, even though the nonstationary nature of many data streams makes it especially appealing. This survey discusses relevant data stream clustering algorithms focusing mainly on fuzzy methods, including their treatment of outliers and concept drift and shift. / Ministero dell‘Istruzione, dell‘Universitá e della Ricerca.

If either the arrival rate or the service rate in an M/M/S queue exhibit variability over time, then no steady state solution is available for examining the system behavior. The arrival and service rates can be represented through Fourier series approximations. This permits numerical approximation of the system characteristics over time. An example of an M/M/S representation of the operations of emergency treatment at Logan Regional hospital is presented. It requires numerical integration of the differential equation for L(t), the expected number of customers in the system at time t.

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In geostatistical analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal covariance function, either directly or through the construction of processes. This task is di cult as these functions should yield positive de nite covariance matrices. In recent years, we have seen a ourishing of methods and theories on constructing spatiotemporal covariance functions satisfying the positive de niteness requirement. The current state-of-the-art when modeling environmental processes are those that embed the associated physical laws of the system. The class of Lagrangian spatio-temporal covariance functions ful lls this requirement. Moreover, this class possesses the allure that they turn already established purely spatial covariance functions into spatio-temporal covariance functions by a direct application of the concept of Lagrangian reference frame. In the three main chapters that comprise this dissertation, several developments are proposed and new features are provided to this special class. First, the application of the Lagrangian reference frame on transported purely spatial random elds with second-order nonstationarity is explored, an appropriate estimation methodology is proposed, and the consequences of model misspeci cation is tackled. Furthermore, the new Lagrangian models and the new estimation technique are used to analyze particulate matter concentrations over Saudi Arabia. Second, a multivariate version of the Lagrangian framework is established, catering to both secondorder stationary and nonstationary spatio-temporal random elds. The capabilities of the Lagrangian spatio-temporal cross-covariance functions are demonstrated on a bivariate reanalysis climate model output dataset previously analyzed using purely spatial covariance functions. Lastly, the class of Lagrangian spatio-temporal cross-covariance functions with multiple transport behaviors is presented, its properties are explored, and its use is demonstrated on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Moreover, the importance of accounting for multiple transport behaviors is discussed and validated via numerical experiments. Together, these three extensions to the Lagrangian framework makes it a more viable geostatistical approach in modeling realistic transport scenarios.

High quality digital images have become pervasive in modern scientific and everyday life — in areas from photography to astronomy, CCTV, microscopy, and medical imaging. However there are always limits to the quality of these images due to uncertainty and imprecision in the measurement systems. Modern signal processing methods offer the promise of overcoming some of these problems by postprocessing these blurred and noisy images. In this thesis, novel methods using nonstationary statistical models are developed for the removal of blurs from out of focus and other types of degraded photographic images. The work tackles the fundamental problem blind image deconvolution (BID); its goal is to restore a sharp image from a blurred observation when the blur itself is completely unknown. This is a “doubly illposed” problem — extreme lack of information must be countered by strong prior constraints about sensible types of solution. In this work, the hierarchical Bayesian methodology is used as a robust and versatile framework to impart the required prior knowledge. The thesis is arranged in two parts. In the first part, the BID problem is reviewed, along with techniques and models for its solution. Observation models are developed, with an emphasis on photographic restoration, concluding with a discussion of how these are reduced to the common linear spatially-invariant (LSI) convolutional model. Classical methods for the solution of illposed problems are summarised to provide a foundation for the main theoretical ideas that will be used under the Bayesian framework. This is followed by an indepth review and discussion of the various prior image and blur models appearing in the literature, and then their applications to solving the problem with both Bayesian and nonBayesian techniques. The second part covers novel restoration methods, making use of the theory presented in Part I. Firstly, two new nonstationary image models are presented. The first models local variance in the image, and the second extends this with locally adaptive noncausal autoregressive (AR) texture estimation and local mean components. These models allow for recovery of image details including edges and texture, whilst preserving smooth regions. Most existing methods do not model the boundary conditions correctly for deblurring of natural photographs, and a Chapter is devoted to exploring Bayesian solutions to this topic. Due to the complexity of the models used and the problem itself, there are many challenges which must be overcome for tractable inference. Using the new models, three different inference strategies are investigated: firstly using the Bayesian maximum marginalised a posteriori (MMAP) method with deterministic optimisation; proceeding with the stochastic methods of variational Bayesian (VB) distribution approximation, and simulation of the posterior distribution using the Gibbs sampler. Of these, we find the Gibbs sampler to be the most effective way to deal with a variety of different types of unknown blurs. Along the way, details are given of the numerical strategies developed to give accurate results and to accelerate performance. Finally, the thesis demonstrates state of the art results in blind restoration of synthetic and real degraded images, such as recovering details in out of focus photographs.