Image Compression:

How Math Led to the JPEG2000 Standard

References and Links

Articles

• JPEG2000, the Next Millenium Compression Standard for Still Images - Proceedings of the IEEE International Conference on Multimedia Computing and Systems, Maryline Charrier, Diego Santa Cruz, Mathias Larsson
• A New Wave in Applied Mathematics - Science Magazine, Barry Cipra
• The Fast Wavelet Transform Beyond Fourier Transforms - Dr. Dobb's Journal of Software Tools, Mac Cody
• Decomposition of Hardy Functions Into Square Integrable Wavelets of Constant Shape - SIAM Journal of Mathematical Analysis, Alexander Grossman and Jean Morlet
• A Method for the Construction of Minimum-Redundancy Codes - Proceedings of the Institute of Radio Engineers, David Huffman
• Multiresolution Approximations and Wavelet Orthonormal Bases of l²(R) - Transactions of the American Mathematical Society, Stephane Mallat
• Plotting and Scheming with Wavelets - Mathematics Magazine, Colm Mulcahy
• The Discrete Cosine Transform - SIAM Review, Gilbert Strang
• Wavelets - American Scientist, Gilbert Strang

Books

• Discovering Wavelets - Edward Aboufadel and Steven Schlicker
• The World According to Wavelets: The Story of a Mathematical Technique in the Making - Barbara Burke Hubbard
• Digital Image Processing, 3rd Edition - Rafael C. Gonzalez and Richard E. Woods
• Wavelets and Operators - Yves Meyer
• The Data Compression Book, 2nd ed. - Mark Nelson and Jean-Loup Gailly.
• Discrete Cosine Transformation: Algorithms, Advantages, Applications - K. Ramamohan Rao and P. Yip
• JPEG2000: Image Compression Fundamentals, Standards and Practice - David Taubman and Michael Marcellin
• Discrete Wavelet Transformations: An Elementary Approach with Applications - Patrick J. Van Fleet
• A Primer on Wavelets and Their Applications, 2nd Edition - James S. Walker

Links

• The Wavelet Digest
• Amara's Wavelet Page
• Wavelets at UST
• JPEG Page
• JPEG2000 Page
• Wikipedia for JPEG2000
• Wikipedia for Wavelets
• Radka Tezaur's Photo Page

• Wavelets and JPEG2000 Home
• Digital Image Basics
• Compression in a Nutshell
• Basic JPEG
  • The Discrete Cosine Tranformation
  • Quantization
  • Color Images
• Wavelet Transformations
  • The Haar Wavelet Transformation
  • General Wavelet Transformations
  • Wavelet Transformations used by JPEG2000
• JPEG2000
  • Features/Enhancements
  • Quantization
• References and Links