Mathematical properties of the JPEG2000 wavelet filters

@article{Unser2003MathematicalPO,
  title={Mathematical properties of the JPEG2000 wavelet filters},
  author={Michael A. Unser and Thierry Blu},
  journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society},
  year={2003},
  volume={12 9},
  pages={
          1080-90
        }
}
  • M. Unser, T. Blu
  • Published 1 September 2003
  • Mathematics
  • IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
The LeGall 5/3 and Daubechies 9/7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. We determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder and Sobolev). We give approximation theoretic quantities such as the asymptotic constant for the L2 error and the angle between the analysis and synthesis spaces which characterizes the loss of performance with respect to an orthogonal projection. We… 
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