[Home] [Book] [Publications] [Multiresolution]
MR/3:

MR/3: 3D and Multichannel Data

MR/3 deals with the analysis of multi-channel data or 3D data.

3D data can either be a real cube, or a set of images of the same observation, but taken at different times. Multi-channel data can be either 1D or 2D multi-channel:

  • 1D multi-channel: a 1D signal is observed at several wavelength or at different times. The result is an image.
  • 2D multi-channel: a 2D signal (image) is observed at several wavelengths or at different times. The result is a cube. A special case of multi-channel images is color images. In this case, we have three channels. Several color coordinate systems exist. The most widely-used is the RGB system. Each pixel is identified by three values R, G, and B corresponding to the three colors red, green, and blue. Applications in MR/3 are
    1. General tools: statistic, operations, noise simulation, conversion ....
    2. Cube and Wavelet transform
      1. 3D a trous wavelet transform and reconstruction.
      2. 3D bi-orthogonal wavelet transform and reconstruction.
      3. 3D Wavelet transform manipulation (band extraction, ...).
      4. 3D data filtering using the wavelet transform.
    3. Multi-channel Data
      1. 1D and 2D Wavelet Karhunen-Loeve transform (WT-KLT) and reconstruction.
      2. 1D and 2D multichannel data filtering using the WT-KLT.
      3. Independent Component Analysis.
    4. Color images
      1. RGB image compression.
      2. RGB image filtering.
      3. RGB image contrast enhancement.
    5. Multi-temporal images
      1. Images coaddition taking into account vertical and horizontal shifts.
      2. Images deconvolution taking into account vertical and horizontal shifts.

    To read further:

    1. J.L. Starck and F. Murtagh, Astronomical Image and Data Analysis , Springer, 2002. (ISBN 3-540-42885-2.; 300-pp. monograph).
    2. J.L. Starck and P. Querre, "Multispectral Image Restoration by the Wavelet-Karhunen-Loeve Transform", Signal Processing , 81, 12, pp 2449-2459, 2001.
    3. J.-L. Starck, E. Pantin and F. Murtagh, "Deconvolution in Astronomy: a Review" , Publication of the Astronomical Society of the Pacific, Vol. 114, pp 1051--1069, 2002.