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:The Electrical Impedance Tomography (EIT) is a computed tomographic technique which provides the images of the spatial distribution of the electrical conductivity or resistivity of a domain under test (DUT) from a set of voltage-current data measured at the boundary of the DUT surrounded by an array of surface electrodes. Due to several advantages, EIT is being applied in several fields of engineering and other applied sciences. In EIT, a PC based EIT instrumentation is required to generate boundary voltage-current data by injecting a constant amplitude low frequency alternating current signal to the DUT. Full set of boundary voltage-current data are sent to the PC and the impedance distribution of the domain are reconstructed using a computer program called image reconstruction algorithm. The reliability, efficiency and image quality depend on the boundary data accuracy which is highly influenced by the instrumentation and data acquisition system. The commercial EIT system manufacturers are limited in numbers and sometimes the commercial EIT systems are developed as application specific devices. Therefore, design and development of laboratory-based standalone EIT systems are found sometimes essential. As the impedance response of material in frequency domain provide a number of material information, multifrequency multifunction EIT (Mf-EIT) systems are proposed and studied by several research groups. In this talk, after introducing the EIT technology and its application, the designing and development of multifrequency instrumentation will be discussed in detail. The electrode switching and data acquisition procedures with different current patterns will be discussed thoroughly. The system interfacing, operation and control by the graphical user interface (GUI) will be summarized. The data processing with amplifiers and filter blocks will be conferred followed by a brief discussion on image reconstruction from the boundary data. The talk will be concluded by a conversation on the present challenges and limitations in EIT instrumentation development.

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. 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]