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

Ronald Raphael Coifman; Lionel J. Woog

doi:10.1117/12.218485

1 September 1995 Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing

Ronald Raphael Coifman, Lionel J. Woog

Proceedings Volume 2567, Investigative and Trial Image Processing; (1995) https://doi.org/10.1117/12.218485
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, 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 example 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) characterised by their duration, pitch, location and amplitude, our method corresponds to transcribing the music in as few notes as possible. The extension to images and video is straightforward we describe the image by collections of oscillatory patterns (paint brush strokes)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 irnages, as well as denoising tools for texture and noise extraction. We start by relating traditional Fourier methods to wavelet, wavelet-packet based algorithms using a recent refinement of the windowed sine and cosine transforms. We will then derive an adapted local sine transform show it's relation to wavelet and wavelet-packet analysis and describe an analysis toolkit illustrating the merits of different adaptive and nonadaptive schemes.

Citation Download Citation

Ronald Raphael Coifman and Lionel J. Woog "Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing", Proc. SPIE 2567, Investigative and Trial Image Processing, (1 September 1995); https://doi.org/10.1117/12.218485

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