wavelet_intro_2005 - Lecture notes of Image Compression and...

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Lecture notes of Image Compression and Video Compression 4. Introduction to Wavelet
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#2 Topics z Introduction to Image Compression z Transform Coding z Subband Coding, Filter Banks z Introduction to Wavelet Transform z Haar, SPIHT, EZW z Motion Compensation z Wireless Video Compression
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#3 Contents z History of Wavelet z From Fourier Transform to Wavelet Transform z Haar Wavelet z Multiresolution Analysis z General Wavelet Transform z EZW z SPIHT
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#4 Wavelet Definition The wavelet transform is a tool that cuts up data, functions or operators into different frequency components, and then studies each component with a resolution matched to its scale ---- Dr. Ingrid Daubechies, Lucent, Princeton U
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#5 Wavelet Coding Methods z EZW - Shapiro, 1993 z Embedded Zerotree coding. z SPIHT - Said and Pearlman, 1996 z Set Partitioning in Hierarchical Trees coding. Also uses “zerotrees”. z ECECOW - Wu, 1997 z Uses arithmetic coding with context. z EBCOT – Taubman, 2000 z Uses arithmetic coding with different context. z JPEG 2000 – new standard based largely on EBCOT z GTW – Hong, Ladner 2000 z Uses group testing which is closely related to Golomb codes z UWIC - Ladner, Askew, Barney 2003 z Like GTW but uses arithmetic coding
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#6 Comparison of Wavelet Based JPEG 2000 and DCT Based JPEG z JPEG2000 image shows almost no quality loss from current JPEG, even at 158:1 compression.
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#7 Introduction to Wavelets z "... the new computational paradigm [wavelets] eventually may swallow Fourier transform methods. .." z " . ..a new approach to data crunching that, if successful, could spawn new computer architectures and bring about commercial realization of such difficult data-compression tasks as sending images over telephone lines. " ---- from "New-wave number crunching" C. Brown, Electronic Engineering Times, 11/5/90.
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#8 Early History of Wavelet Theory z Roots found in a variety of disciplines z Mathematics, Signal Processing, Computer Vision, Physics. z 1910 Haar basis z First wavelet. z 1946 The Gabor transform z Short time Fourier transform with Gaussian window function. z 1964 Calderon's work on singular integral operators z Contains the continuous wavelet transform. z 1971 A. Rosenfeld and M. Thurston z Multi-resolution techniques invented in machine vision z Multi-resolution schemes inherent in the wavelet transform. z 1976 A. Croiser, D. Estaban, C. Galand z Quadrature mirror filter banks for speech coding z Digital implementation of wavelets.
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#9 Recent History of Wavelets z 1984 J. Morlet and A. Grossman z ‘‘Invent“ term wavelets z Apply them to the analysis of seismic signals z 1985 Meyer z tried to prove that no orthogonal wavelet other than Haar exists, found one by trial and error! z 1987 Mallat z Developed multiresolution theory, DWT, wavelet construction techniques (but still noncompact) z 1988 I. Daubechies z Found compact, orthogonal wavelets with arbitrary number of vanishing moments!
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This note was uploaded on 06/09/2011 for the course CAP 5015 taught by Professor Mukherjee during the Spring '11 term at University of Central Florida.

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wavelet_intro_2005 - Lecture notes of Image Compression and...

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