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 15

Abstract: Electrical impedance tomography (EIT) has been widely studied for use in pulmonary imaging applications, and the inclusion of prior-known spatial information from thoracic CT scans has been demonstrated to improve pulmonary EIT images. However, obtaining a CT scan has a number of drawbacks to the patient, including ionizing radiation, expense, and a need to move the patient to the machine. Ultrasound tomography (UST), on the other hand, does not have these drawbacks, but has only been minimally studied for use in pulmonary imaging due to difficulties with wave propagation. Low-frequency UST, however, has the potential to propagate in lung tissue, and therefore may be suitable for use as a prior in EIT. In this talk, we present numerically simulated results demonstrating the potential use of UST as a spatial prior in pulmonary EIT imaging.

Feb. 13 | TBA | TBA |

Feb. 27 | TBA | TBA |

Mar. 5 | TBA | Samuli Siltanen, University of Helsinki, Finland |

Mar. 12 | TBA | Alexei Novikov, Penn State |

Apr. 2 | How to solve Bayesian inverse problems in practice | Wolfgang Bangerth, Dept. of Math., CSU |

Apr. 9 | Reconstruction of a conductivity inclusion using the Faber polynomials | Mikyoung Lim, KAIST, Seoul Korea |

Apr. 23 | TBA | Paulina Vosolov, Dept. of Math., RPI |

Sept. 5 | Sparsity-Based Inpainting and Data Separation | Emily King, Dept. of Math., CSU |

Sept. 19 | A hybrid approach combining analytical and iterative regularization methods for Electrical Impedance Tomography and Diffuse Optical Tomography problems | Sanwar Ahmad, Dept. of Math., CSU |

Oct. 17 | Rescheduled to Oct. 31 | Roozbeh Gharakhloo, Dept. of Math., CSU |

Oct. 31 | A Riemann-Hilbert approach to asymptotic analysis of a bordered Toeplitz determinant and the next-to-diagonal correlations of the anisotropic square lattice Ising model. | Roozbeh Gharakhloo, Dept. of Math., CSU |

Nov. 7 | No Seminar - Math Day | |

Nov. 14 | Spectral approaches to d-bar systems | Christian Klein, Mathematics Institute of Bourgogne, France |

Nov. 21 | Pulmonary Imaging using Electrical Impedance Tomography with a Low-Frequency Ultrasound Prior | Melody Alsaker, Gonzaga University |

Abstract (pdf)

[Spring 2015] [Fall 2014]