Micrological analysis, smooth frames and denoising in Fourier space

  • Authors:

  • Ryuichi Ashino;Steven J. Desjardins;Christopher Heil;Michihiro Nagase;Rémi Vaillancourt

  • Affiliations:

  • Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan;Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada KIN 6N5;School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia;Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan;Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5

  • Venue:
  • Focus on computational neurobiology
  • Year:
  • 2004

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Abstract

Microlocal filtering is performed with adapted orthonormal multiwavelets and smooth frame multiwavelets in Rn. The values of the wavelet coefficients of a function give a rough estimate of its microlocal content, as shown by an example. Multidirectional denoising of images is presented as the action of a pseudodifferential operator which is the product of directional diffusion equations.