Wavelets from a statistical perspective / Maarten Jansen

By:

Jansen, Maarten

Material type: Text

TextLanguage: English Publication details: Boca Raton : CRC Press, 2022.Edition: 1st edDescription: xii, 325 p.: ill., (black and white) ; 24 cmISBN:

9781032200675

Subject(s):

DDC classification:

23 515.243 JAN

Contents:

1. Wavelets: nonlinear processing in multiscale sparsity. 2. Wavelet building blocks. 3. Using lifting for the design of a wavelet transform. 4. Wavelet transforms from factored refinement schemes. 5. Dyadic wavelets. 6. Dyadic wavelet design in the frequency domain. 7. Design of dyadic wavelets. 8. Approximation in a wavelet basis. 9. Overcomplete wavelet transforms. 10. Two-dimensional wavelet transforms. 11. The multiscale local polynomial transform. 12. Estimation in a wavelet basis.

Summary: Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
General Books	CUTN Central Library Sciences	Non-fiction	515.243 JAN (Browse shelf(Opens below))	Available		47639

1. Wavelets: nonlinear processing in multiscale sparsity.
2. Wavelet building blocks.
3. Using lifting for the design of a wavelet transform.
4. Wavelet transforms from factored refinement schemes.
5. Dyadic wavelets.
6. Dyadic wavelet design in the frequency domain.
7. Design of dyadic wavelets.
8. Approximation in a wavelet basis.
9. Overcomplete wavelet transforms.
10. Two-dimensional wavelet transforms.
11. The multiscale local polynomial transform.
12. Estimation in a wavelet basis.

Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material

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