Wavelet Frames And Orthonormal Wavelets With Compact Support For Sparse Decompositions
Author
Henriksen, Peter Løfqvist
Term
4. term
Education
Publication year
2020
Submitted on
2020-06-02
Pages
99
Abstract
Dette speciale introducerer begrebet frames, en fleksibel måde at repræsentere data på, og wavelet frame-transformationen. Det forklarer, hvordan sådanne frames kan konstrueres ved hjælp af oblique extension principle, et konstruktionsprincip til at opbygge wavelet-systemer. Med denne konstruktion præsenteres den diskrete wavelet frame-transformation sammen med den diskrete ortonormale wavelet-transformation. Til sidst sammenlignes de to transformationer med eksempler, der viser, hvordan de kan reducere støj.
This thesis introduces frames, a flexible way to represent data, and the wavelet frame transform. It explains how to construct such frames using the oblique extension principle, a design method for building wavelet systems. Based on this construction, it presents the discrete wavelet frame transform alongside the discrete orthonormal wavelet transform. Finally, it compares the two using noise reduction examples to illustrate how each approach handles denoising.
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