Atomic decomposition and completion of moment sequences: from super-resolution to tensor factorization
Date and time:
Monday, December 7, 2015 - 4:00pm
Modern data analysis relies on identifying complex, nonlinear models from noisy and incomplete data. Several of such tasks can be formulated and analyzed as linear inverse problems involving moments, expectations of monomials against usually discrete measures with small supports. The best convex regularizers for such inverse problems are given by the corresponding atomic norms. I will focus on two instances of moment inverse problems, super-resolution in imaging and tensor factorization in machine learning. For super-resolution, I will discuss how the atomic norm allows one to recover precise high-frequency details of point sources from a minimal number of low-frequency observations. I will also present how to deal with non-stationary unknown point spread functions using the lifting idea, leading to a method of blind super-resolution. For tensors, I will present results on overcomplete tensor decomposition and discuss how this will help solve tensor inverse problems in an optimal way.