Mathematics Awareness Week - April 1998

Mathematics and Imaging

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Theme Poster


The image on this page can be downloaded and used freely for non-commercial purposes as long as proper credit is given to:

  • The Joint Policy Board for Mathematics
  • Ronald Coifman, Yale University
  • Francois Meyer, Yale University

  • Image captions, left side:
    1. Original
    2. Wavelet
        300:1 compression
        Preserves all but fine structure
    3. Wavelet packet basis
        30:1 compression
        Preserves fine structure of bristles
    4. Residual
    Text block, lower left:
    The original image is the sum of the three. Each pulls out different features of the original. We can think of the image as being synthesized by three different instruments, in a way similar to a musical orchestration where the final sound is the sum of the notes from each instrument.

    This mathematical transcription is useful for a more efficient and accurate storage and processing of imaging data, but also provides tools for denoising and identifying structure in images. For example, it can sharpen detail in medical images, such as MRI, and be used to identify particular objects for diagnostic purposes.
    Text block, lower right:
    Sponsored by the:
    Joint Policy Board for Mathematics:
    American Mathematical Society
    Mathematical Association of America
    Society for Industrial and Applied Mathematics
    Informs
    http://www.mathaware.org/maw/
    Images provided by Ronald Coifman, Yale University
    Francois Meyer, Assistant Professor of diagnostic radiology, Yale University school of medicine, and computer science at Yale. Meyer was responsible for the processing of the images.

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