Multiscale Signal Analysis and Modeling

This book surveys advances in multiscale analysis using wavelets and other systems: sinc functions, discrete Hermite functions and more, and offers applications in filter design, sampling, signal and image representation/transmission and other methods.

Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Discusses recently developed signal modeling techniques, such as the multiscale method for complex time series modeling, multiscale positive density estimations, Bayesian Shrinkage Strategies, and algorithms for data adaptive statistics Introduces new sampling algorithms for multidimensional signal processing Provides comprehensive coverage of wavelets with presentations on waveform design and modeling, wavelet analysis of ECG signals and wavelet filters Reviews features extraction and classification algorithms for multiscale signal and image processing using Local Discriminant Basis (LDB) Develops multi-parameter regularized extrapolating estimators in statistical learning theory

Inhalt

Part I Sampling.- Convergence and Summability of Cardinal Series.- Improved Approximation via Use of Transformations.- Generalized Sampling In L2(Rd) Shift-Invariant Subspaces With Multiple Stable Generators.- Function Spaces for Sampling Expansions.- Coprime Sampling And Arrays In One And Multiple Dimensions.- Chromatic Expansions and the Bargmann Transform.- Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems.- Constructions and a generalization of perfect autocorrelation sequences on Z.- Part II Multiscale Analysis.- A unified theory for multiscale analysis of complex time series.- Wavelet Analysis of ECG Signals.- Multiscale signal processing with discrete Hermite functions.- Local Discriminant Basis Using Earth Mover's Distance Earth Mover's Distance Based Local Discriminant Basis.- Part III statistical Analysis.- Characterizations of Certain Continuous Distributions.- Bayesian Wavelet Shrinkage Strategies - A Review.- Multi-parameter regularization for construction of extrapolating estimators in statistical learning theory.