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URN etd-0614117-145650
Author Ting-Chieh Tsai
Author's Email Address No Public.
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Department Applied Mathematics
Year 2016
Semester 2
Degree Master
Type of Document
Language English
Title JPEG 2000 Image Compression Method: Biorthogonal Wavelets and Lifting Transform
Date of Defense 2017-06-20
Page Count 102
Keyword
  • lifting transform
  • biorthogonal wavelet
  • discrete wavelet transform
  • image compression
  • JPEG 2000
  • Abstract Image compression is an important aspect of image processing. In 1992 the Joint Photographic
    Experts Group announced the JPEG Standard algorithm. The related software jpg
    has become one of the most popular file format for still image compression in smart phones and
    digital cameras. In 2000, they announced the algorithm JPEG 2000, an important improvement
    of JPEG Standard in terms of compression rate and flexibility.
    Both algorithms consist of the four steps: Pre-processing, Transformation, Quantization
    and Encoding. In this thesis, we shall study the general algorithm of JPEG 2000. Special emphasis
    will be made on the discrete wavelet transform in the Transformation step. In particular,
    we shall study with mathematical rigor orthogonal wavelets and biorthogonal wavelets CDF
    9/7, plus a related lifting transformation, developed by Daubechies-Sweldens. They form an
    important part in the lossy compression algorithm of JPEG 2000, respectively. Our material
    comes from several monographs, notably the book ‘Discrete Wavelet Transformations’ by Van
    Fleet, and the paper [4], with the help of the classical monographs by Daubechies [3] and Mallat
    [6]. The materials are organized into a self-contained and systematic manner. We also write
    some programs with Mathematica to exemplify the biorthogonal wavelet transform and lifting
    transform.
    Advisory Committee
  • Hsin-Yuan Huang - chair
  • Tsung-Lin Lee - co-chair
  • Chao-Kai Wen - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0614117-145650.pdf
  • indicate access worldwide
    Date of Submission 2017-07-14

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