Inverse problems is a field of mathematics comprised of many areas including analysis, modeling, PDE's and scientific computation. Inverse problems arise in abundance in engineering, biology, physics, geophysics and more. This seminar addresses fundamental topics in inverse problems in a variety of applications.

Regular meeting times & location: Thursdays at 2 pm in Weber 223

Abstract: Fundamental answers about small planetary bodies (comest and asteroids) origin and evolution hinge on our ability to image in detail their interior structure in 3D and at high resolution. The interior structure is not easily accessible without redundant data, e.g., radar reflections observed from multiple viewpoints, as in medical tomography. The Comet Radar Explorer mission aims to acquire a dense network of in-phase radar echoes from orbit to obtain a high resolution 3D image of comet Tempel 2's interior. Full wavefield inversion facilitate high quality imaging of the comet interiors, particularly if the comet nucleus is characterized by complex structure and large contrasts of physical properties. Knowledge of the comet shape and all-around orbital radar acquisition enable accurate and computationally-efficient 3D tomography. Using realistic numerical experiments, I will argue that (1) interior comet imaging is intrinsically 3D and conventional SAR processing does not satisfy imaging/resolution requirements; (2) interior tomography can be performed progressively with data acquired through successive orbits around the comet; (3) exploiting the known exterior shape of the comet facilitates cost-effective wavefield tomography; (4) multiscale wavefield tomography provides detailed information about the 3D internal physical properties; (5) imaging resolution exceeds the wavelength limits corresponding to low-frequency radar waves; (6) monostatic tomography yields 3D models comparable with what could be accomplished by more complex systems.

Jan. 18 | Computational Uncertainty Quantification for Inverse Problems | Johnathan Bardsley, University of Montana |

Feb. 1 | Electrical Impedance Tomography (EIT) Instrumentation: A Journey Through Design, Development, and Applications | Tushar Kanti Bera, Dept. of Medical Imaging, University of Arizona |

Mar. 8 | Improving Electrical Impedance Tomography with Robust D-bar Methods | Sarah Hamilton, Marquette University |

Mar. 29 | TBA | Randy Bartels, Colorado State University |

April 12 | Wavefield tomography of comet interiors | Paul Sava, Colorado School of Mines |

Aug. 24 | Electrical impedance tomography imaging via the Radon transform | Samuli Siltanen, University of Helsinki |

Sept. 7 | no seminar - JM at IMA | |

Sept. 20 | The enclosure method for the anisotropic PDEs | Yi-Hsuan Lin, University of Washington |

Oct. 12 | Forward and inverse problems in geodynamic modelling: Part I -- Evolution of island chains in the South Atlantic and Indian Ocean | Rene Gassmoeller, CSU |

Oct. 26 | Forward and inverse problems in geodynamic modelling: Part II -- Thermochemical Convection | Juliane Dannberg, CSU |

Nov. 2 | no seminar - Math Day | |

Nov. 9 | Monte Carlo methods for radiative transfer with singular kernels | Olivier Pinaud, CSU |

Nov. 16 | Inverse problems and integrable PDEs | Kenneth McLaughlin, CSU |

[Spring 2015] [Fall 2014]