Fast Multipole Methods and Large-Scale Inverse Problems

Abstract: 

Fast Multipole Methods and Large-Scale Inverse Problems

This work falls into two broad categories:

  • Developing fast multipole methods for updating the electrostatic potential of a collection of point charges. This has applications in computational chemistry, molecular dynamics, and protein folding.
  • Large-scale optimization problems in inverse problems in imaging. This work seeks to reconstruct images from noisy and blurred data using physics-based models of the imaging system. Some applications are high-dynamic range imaging, digital holography for long-range remote sensing, and magnetic resonance encephalography.

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