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Topics in Inverse Problems and Data Assimilation


Inverse Problems

Theory of Regularization

Source Reconstruction

  • Uniqueness, Non-Uniqueness and Stability Results
  • Reconstruction of Acoustic Sources
  • Reconstruction of Currents
  • Magnetic Tomography

Inverse Scattering

  • Uniqueness and Stability Result
  • Iterative Reconstruction Methods
  • Sampling and Probing Methods
  • Time-Domain Methods

Image Reconstruction

  • Denoising
  • Filtering

Computerized Tomography (CT)

  • Classical CT
  • Radon Transform
  • Limited Aperture CT
  • GPS/GNSS Tomography

Optical Diffusion Tomography (ODT)

  • Uniqueness and Stability Results
  • Methods for ODT

Heat Transfer Inverse Problems

  • Uniqueness and Stability Results
  • Reconstruction of Heat Functions

Inverse Fluid Dynamics

  • Uniqueness and Stability Results
  • Flow Reconstruction Methods

mpe2013.jpg calipso02.jpg calipso03.jpg

Data Assimilation and Dynamical Inverse Problems

Theory of Data Assimilation

  • Uniqueness
  • Stability
  • Controlability

Methods for Data Assimilation

  • Optimal Interpolation
  • Three-Dimensional Variational Data Assimilation (3dVar)
  • Four-Dimensional Variational Data Assimilation (4dVar)
  • Kalman Filter
  • Ensemble Kalman Filter (e.g. EnKF, LETKF)
  • Bayesian Methods
  • Markov Chain Monte Carlo (MCMC)
  • Particle Filters (e.g. SIR)
  • Gaussian Mixture Models

Measurement Classes in Data Assimilation

  • In-Situ Measurements
  • Radar Measurements
  • Radiances
    • Infrared Sounders
    • Microwave Sounders
    • Radiances over Land
    • Cloudy Radiances
  • GPS/GNSS Measurements
  • Radio-Occultations
  • INSPIRE DIRECTIVE - Infrastructure for Spatial Data: inspire.
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topics.txt · Last modified: 2014/07/29 22:14 by potthast