Wavelet

This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.

This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames,

This voluve investigats the use of the progressive regressive strategy for biometrical authentication; the best wavelet packet based selection algorithm and its application in image denoising; the application of the empirical wavelet transform for seismic anomalies detection in ultralow-frequency geomagnetic signals.

This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers.

This book presents a succinct compendium of some of the more recent variants of Discrete Wavelet Transform (DWT) and their use to come up with solutions to an array of problems transcending the traditional application areas of image/video processing and security to the relatively newer areas of medicine, artificial intelligence, power systems and telecommunications.

This book delves into an exposition on spectral analysis, restoring, monitoring, and signal processing, as well as essential applications required in waveguides and for the improvement of medical images, proving the wavelet transform to be helpful in resolution analysis in time-frequency, with an emphasis on different methods of the calculus using FFT and DSTFT.