Adapted waveform analysis, wavelet-packets, and local cosine libraries

Ronald Raphael Coifman

doi:10.1117/12.131583

1 November 1992 Adapted waveform analysis, wavelet-packets, and local cosine libraries

Ronald Raphael Coifman

Proceedings Volume 1826, Intelligent Robots and Computer Vision XI: Biological, Neural Net, and 3D Methods; (1992) https://doi.org/10.1117/12.131583
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

Adapted wave form analysis, refers to a collection of FFT like adapted transform algorithms. Given a signal or an image these methods provide a special orthonormal basis relative to which the image is well represented. The selected basis functions are chosen inside predefined libraries of oscillatory localized functions (waveforms) so as to minimize the number of parameters needed to describe our object. These algorithms are of complexity N log N opening the door for a large range of applications in signal and image processing, such as compression, feature extraction and enhancement. Our goal is to describe and relate traditional Fourier methods to wavelet, wavelet-packet based algorithms by making explicit their relative role in analysis. Starting with a recent refinement of the windowed sine and cosine transforms we will derive an adapted local sine transform, show it''s relation to wavelet and wavelet- packet analysis and describe an analysis tool-kit illustrating the merits of different adaptive and non-adaptive schemes.

Citation Download Citation

Ronald Raphael Coifman "Adapted waveform analysis, wavelet-packets, and local cosine libraries", Proc. SPIE 1826, Intelligent Robots and Computer Vision XI: Biological, Neural Net, and 3D Methods, (1 November 1992); https://doi.org/10.1117/12.131583

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