|F Feb 25|
|Feb 21||Presidents’ Day (University Holiday)||No seminar|
|M Feb 28|
|F Mar 11||Eric Todd Quinto||Microlocal analysis of Fourier Integral Operators in scattering tomography
We present a novel microlocal analysis of generalized Radon transforms that describe the integrals of functions of compact support over curves in the plane and surfaces of revolution of smooth curves in higher dimensional spaces. We show that the Radon transforms satisfy important properties that show that the reconstruction operator should image visible features of objects and not add artifacts. We introduce microlocal analysis, the math behind our results.
Our results apply to models in Emission Compton Scattering Tomography (ECST) and Bragg Scattering Tomography (BST). We show that the ECST and BST integration curves or surfaces in general satisfy the conditions to not produce artifacts. We provide simulated reconstructions from ECST and BST data to illustrate our points. Additionally, we give “sinusoidal” integration curves which do not satisfy the assumptions, and we provide simulations of the image artifacts. The observed artifacts in reconstruction are shown to align exactly with our predictions.
This is joint work with James Webber (Brigham and Women’s Hospital, formerly Tufts University).
|F Apr 1||Kasso Okoudjou||On a very fun and addictive problem: The HRT Conjecture
Pick your favorite square integrable function defined on the real line (you may assume that is a Schwartz class function). Is the set linearly independent in for each ?This a special case of a conjecture put forth in 1996 by C. Heil, J. Ramanatha, and
|F May 6||Mostafa Maslouhi||Some results and open problems on Frames and Probabilistic Frames
In this talk we present a solution of two open problems posed in (Ehler and Okoudjou, 2013) related to the representation of Positive Operators Valued Measures (POVM) by means of tight probabilistic frames in and how far is the closest probabilistic tight frame from a given probability measure in , where the distance here is the quadratic Wasserstein metric used for optimal transportation problem for measures. For the first problem we characterize all the POVM representable by means of a tight probabilistic frames in and for the second, we solve the optimization problem