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 weekly seminar addresses fundamental topics in inverse problems in a variety of applications.

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

Abstract: We consider here some inverse coefficient problems for the transport equation with multiple internal data sets. Such problems find applications in recent hybrid imaging modalities such as (fluorescence) photoacoustic tomography. We will discuss some theoretical results on the uniqueness and stability of the inverse problems and propose some efficient reconstruction strategies which we demonstrate with numerical simulations.

Jan. 29 | no seminar | |

Feb. 5 | Regularization of the Inverse Scattering Problem using Shearlet Frames | Gitta Kutyniok,Technical University, Berlin |

Feb. 12 | no seminar | |

Feb. 19 | no seminar | |

Feb. 26 | A Novel Regularization Technique for Electrical Impedance Tomography in an Open Half-Space Domain | Ethan Murphy, Dartmouth University |

March 5 | Seismic Tomography; Past, Present, and Future | Rick Aster, Dept. of Geosciences,CSU |

March 12 | Colored Buzz, or Glottal Inverse Filtering | Samuli Siltanen, University of Helsinki, Finland |

March 26 | Seeing Beyond the Diffraction Limit | Peijun Li, Purdue University |

April 2 | no seminar | |

April 9 | Title: Inverse Transport Problems with Internal Data and Applications | Kui Ren, University of Texas at Austin |

April 16 | no seminar | |

April 23 | no seminar | |

April 30 | TBA |

Human speech is a sophisticated means of communication and plays an unparalleled role in today's society. Whether developing the latest voice recognition software for a smartphone or designing computers to aid people who have lost their voice through disease and illness, researchers are finding ways to map the precise mechanisms in the human vocal tract.

Through a number of practical demonstrations, it is shown how the human vocal folds and the mouth and lips combine to create the vowel sound. Furthermore, it is explained how a technique called glottal inverse filtering (GIF) can be used to determine the exact mechanisms behind vowel sounds from microphone recordings.

The main use of improved GIF is to provide disabled women and children with better computer-based speech prostheses. The higher fundamental frequency of women's and children's voices makes them more difficult for speech synthesis software. Using Bayesian inversion and Markov chain Monte Carlo (MCMC) method, we can significantly improve GIF results over traditional engineering approaches for challenging speech signals.