- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 2, 2017 - 1:55pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Weilin Li – University of Maryland, College Park – wl298@math.umd.edu – https://www.math.umd.edu/~wl298/
- Organizer
- Wenjing Liao
We formulate
super-resolution as an inverse problem in the space of measures, and
introduce a discrete and a continuous model. For the discrete model, the
problem is to accurately recover a sparse high dimensional vector from
its noisy low frequency Fourier coefficients. We determine a sharp bound
on the min-max recovery error, and this is an immediate consequence of a
sharp bound on the smallest singular value of restricted Fourier
matrices. For the continuous model, we study the total variation
minimization method. We borrow ideas from Beurling in order to determine
general conditions for the recovery of singular measures, even those
that do not satisfy a minimum separation condition. This presentation
includes joint work with John Benedetto and Wenjing Liao.