# Inverse problems

Wednesday, October 16, 2019 - 11:20am - 12:05pm

Jong Chul Ye (Korea Advanced Institute of Science and Technology (KAIST))

Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning approaches for inverse problems thanks to its excellent performance. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance.

Thursday, October 17, 2019 - 4:15pm - 5:00pm

Florian Knoll (NYU Langone Medical Center)

In this talk, I will provide an introduction to the use of machine learning and convolutional neural networks (CNNs) in the area of MR image reconstruction. Building on a general framework of inverse problems and variational optimization, I will focus on application examples from image reconstruction for accelerated Magnetic Resonance (MR) imaging. I will cover both methodological developments as well as clinical translation and validation.

Wednesday, May 1, 2019 - 10:10am - 11:00am

Francois Monard (University of California, Santa Cruz)

In this talk, we will review prior and recent work on the reconstruction of (1) an isotropic kernel, or (2) a source term, in the radiative transfer equation from measured outgoing radiation.

Friday, September 8, 2017 - 10:40am - 11:15am

Luis Tenorio (Colorado School of Mines)

Since in Bayesian inversion data are often informative only on a low-dimensional subspace of the parameter space,

significant computational savings can be achieved using such subspace to characterize and approximate the posterior distribution of the parameters.

We study approximations of the posterior covariance matrix defined as low-rank updates of the prior covariance matrix and

prove their optimality for a broad class of loss functions which includes the Forstner

significant computational savings can be achieved using such subspace to characterize and approximate the posterior distribution of the parameters.

We study approximations of the posterior covariance matrix defined as low-rank updates of the prior covariance matrix and

prove their optimality for a broad class of loss functions which includes the Forstner

Wednesday, September 6, 2017 - 2:55pm - 3:30pm

Youssef Marzouk (Massachusetts Institute of Technology)

Many inverse problems may involve a large number of observations. Yet these observations are seldom equally informative; moreover, practical constraints on storage, communication, and computational costs may limit the number of observations that one wishes to employ. We introduce strategies for selecting subsets of the data that yield accurate approximations of the inverse solution. This goal can also be understood in terms of optimal experimental design.

Thursday, February 16, 2017 - 10:15am - 11:05am

Faouzi Triki (Université Grenoble-Alpes)

In the talk I will present recent results on multifrequency electrical impedance tomography. The inverse problem consists in identifying a conductivity inclusion inside a homogeneous background medium by injecting one current. I will use an original spectral decomposition of the solution of the forward conductivity problem to retrieve the Cauchy data corresponding to the extreme case of perfect conductor.

Thursday, February 16, 2017 - 11:30am - 12:20pm

Francis Chung (University of Kentucky)

The standard problem of optical tomography is to obtain information about the optical properties of an object by making measurements on the boundary. Acousto-optic tomography is a variation of this problem where the object is perturbed by an acoustic field, and optical boundary measurements are taken as the parameters of the acoustic field vary. In this talk I'll give a short introduction to the idea of acousto-optic tomography, and discuss some inverse problems that arise from this imaging technique.

Tuesday, February 14, 2017 - 11:30am - 12:20pm

P. Scott Carney (University of Illinois at Urbana-Champaign)

Optical coherence tomography (OCT) provides an alternative to physical sectioning that allows for imaging of living samples and even in vivo examination of cell structure and dynamics. There is, in the OCT community, a widely held belief that there exists a trade-off between transverse resolution and the thickness of the volume that may be imaged with a fixed focal plane. Efforts to overcome this trade-off have focused on the design optical elements and imaging hardware.

Friday, June 10, 2016 - 9:00am - 10:00am

Benham Jafarpour (University of Southern California)

In this talk, I will present an overview of sparse representations and their applications in solving inverse modeling problems involving PDEs that describe multi-phase flow in heterogeneous porous media. The related PDE-constrained inverse problems are often formulated to infer spatially distributed material properties from dynamic response measurements at scattered source/sink locations.

Thursday, June 9, 2016 - 9:00am - 10:00am

Paul Barbone (Boston University)

Inverse problems are often formulated as constrained optimization problems. The constraint is in the form of a forward problem. The forward model is repeatedly solved and iteratively updated in order to bring its predictions in conformity with a set of data, or observations. We identify two distinct classes of deficiencies present in standard forward solvers (i.e. variational formulations) when used in this way. These deficiencies has motivated the development of two new variational formulations to address them.