An introduction to our ELEC 301 project.
A brief description of the discrete wavelet transform, and the two-dimensional discrete wavelet transform.
This is the "core" module for Group 2 from which you can find links to all our other modules.
This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from Calculus and Differential Equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.
Discrete-time implementation of the DWT.
This module focus on search for better filters/wavelets.
This module gives an overview of wavelets and their usefulness as a basis in image processing. In particular we look at the properties of the Haar wavelet basis.
This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.
Basic introduction to splines. Link to other modules.
The course focuses on the problem of supervised learning within the framework of Statistical Learning Theory. It starts with a review of classical statistical techniques, including Regularization Theory in RKHS for multivariate function approximation from sparse data. Next, VC theory is discussed in detail and used to justify classification and regression techniques such as Regularization Networks and Support Vector Machines. Selected topics such as boosting, feature selection and multiclass classification will complete the theory part of the course. During the course we will examine applications of several learning techniques in areas such as computer vision, computer graphics, database search and time-series analysis and prediction. We will briefly discuss implications of learning theories for how the brain may learn from experience, focusing on the neurobiology of object recognition. We plan to emphasize hands-on applications and exercises, paralleling the rapidly increasing practical uses of the techniques described in the subject.
IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.
An overview of the methods used in the original paper.
In order to find a solution to the basic recursion equations, the scaling filter must satisfy a set of sufficient conditions. Certain conditions on the scaling filter will directly result in a wavelet expansion system with certain properties.
Wavelets are an alternative tool for signal decomposition using orthogonal functions. Unlike basic Fourier analysis, wavelets do not lose completely time information, a feature that makes the technique suitable for applications where the temporal location of the signal’s frequency content is important. One of the fields where wavelets have been successfully applied is data analysis. In particular, it has been demonstrated that wavelets produce excellent results in signal denoising i.e. the removal of noise from an unknown signal. Shrinkage methods for noise removal, first introduced by Donoho in 1993, have led to a variety of approaches combining wavelets with probabilistic concepts leading to new efficient denoising procedures. This work presents a summary of basic methods for noise removal. Their main features and limitations are discussed and a comparison study is developed. A signal contaminated with Gaussian additive noise is used as testbed for the methods. Conclusions on the performance of the methods, based upon computational efficiency and number of terms used for decomposition, are presented.
Wavelet systems are the expansion of functions into a set of weighted scaling and wavelet functions, which are localized in time and frequency. They provide a multiresolution analysis of a given signal.
Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.
On well-known property of valid scaling functions in wavelet analysis is that the scaling functions can perfectly reproduce a polynomial of degree no more than the wavelet smoothness. This property can be easily derived using the Unser-Blu Scaling Function / Spline Factorization Theorem.
