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: We consider the problem of imaging sparse scenes from a few noisy data using an l1-minimization approach. This problem can be cast as a linear system of the form Ax=b. The dimension of the unknown sparse vector x is much larger than the dimension of the data vector b. The l1-minimization alone, however, is not robust for imaging with noisy data. To improve its performance we propose to solve instead the augmented linear system [A|C]x=b, where the matrix C is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data can be well approximated with high probability. This approach gives rise to a new parameter-free imaging method that has a zero false discovery rate for any level of noise. We also obtain exact support recovery if the noise is not too large.

Mar. 5 | Electrical impedance tomography, enclosure method and machine learning | Samuli Siltanen, University of Helsinki, Finland |

Mar. 12 | Imaging with incomplete and corrupted data | 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 - Rescheduled to the fall semester | Mikyoung Lim, KAIST, Seoul Korea |

Apr. 16 | A Mathematical Approach to Neuronal Network Reconstruction | 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]