Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing

Ronald Raphael Coifman

doi:10.1117/12.162053

1 November 1993 Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing

Ronald Raphael Coifman

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162053
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Adapted wave form analysis, refers to a collection of FFT like adapted transform algorithms. Given an image these methods provide special matched collections of templates (orthonormal bases) enabling an efficient coding of the image. Perhaps the closest well known examples of such coding method is provided by musical notation, where each segment of music is represented by a musical score made up of notes (templates) characterized by their duration, pitch, location and amplitude, our method corresponds to transcribing the music in as few notes as possible. The extension of images and video is straightforward. We describe the image by collections of oscillatory patterns of various sizes, locations and amplitudes using a variety of orthogonal bases. These selected basis functions are chosen inside predefined libraries of oscillatory localized functions (trigonometric and wavelet-packets waveforms) so as to optimize 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 denoising and enhancement. In particular we describe a class of special purpose compressions for fingerprint images, as well as denoising tools for texture and noise extraction.

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Ronald Raphael Coifman "Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162053

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