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A Mathematical Theory For Learning, And Its Application To Time-Varying Computed Tomography

Author

Listed:
  • LEONID PERLOVSKY

    (Sensors Directorate, Air Force Research Laboratory, 80 Scott Drive, Hanscom AFB, MA 01731, USA)

  • ROSS DEMING

    (Anteon Corporation, Air Force Research Laboratory, Sensors Directorate, 80 Scott Drive, Hanscom AFB, MA 01731, USA)

Abstract

The brain has evolved to enable organisms to survive in a complicated and dynamic world. Its operation is based upona priorimodels of the environment which are adapted, during learning, in response to new and changing stimuli. The same qualities that make biological learning mechanisms ideal for organisms make their underlying mathematical algorithms ideal for certain technological applications, especially those concerned with understanding the physical processes giving rise to complicated data sets. In this paper, we offer a mathematical model for the underlying mechanisms of biological learning, and we show how this mathematical approach to learning can yield a solution to the problem of imaging time-varying objects from X-ray computed tomographic (CT) data. This problem relates to several practical aspects of CT imaging including the correction of motion artifacts caused by patient movement or breathing.

Suggested Citation

  • Leonid Perlovsky & Ross Deming, 2005. "A Mathematical Theory For Learning, And Its Application To Time-Varying Computed Tomography," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 147-171.
    • Handle: RePEc:wsi:nmncxx:v:01:y:2005:i:01:n:s1793005705000081
    DOI: 10.1142/S1793005705000081
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