Sparse blind deconvolution arises in a variety of imaging problems, including deblurring and motif-finding in microscopy data. Inspired by these applications, we study the short-and-sparse variant of this problem, in which the goal is to recover a short filter and a (random) sparse spike train from their convolution. We describe theory for methods based on nonconvex optimization over the sphere, which guarantee that we can efficiently produce the ground truth, up to symmetry.

This presentation is part of Minisymposium “MS21 - Recent mathematical advances in phase retrieval and computational imaging (2 parts)”
organized by: Mahdi Soltanolkotabi (University of Southern California) , Tamir Bendory (Princeton University) .

Authors:

John Wright (Department of Electrical Engineering, Columbia University)

Yuqian Zhang (Columbia University)

Han-Wen Kuo (Columbia University)

Keywords:

image deblurring, inverse problems, nonlinear optimization