Wavelets are useful for many applications including signal/image processing. Tensor product has been a predominant method in constructing multivariate wavelets. In this talk, I will first provide a brief overview of the wavelet analysis and the use of tensor product in constructing multivariate wavelets. Then I will introduce a new alternative to tensor product, to which we refer as Coset Sum. We will discuss the similarity and difference between the two methods. We will also see that some of known limitations of tensor product can be overcome by Coset Sum, albeit in a limited sense.

Nonsmooth optimization problems are generally considered to be more difficult than smooth problems. Among those, optimization problem with sparsity, which has wide applicability in machine learning, satistics, and image processing, are usually structured. Hence many efficient optimization methods have been developed to solve such problems. In this talk, we introduce several optimization problems with sparsity arising in applications and optimization methods for solve them.

Basic concepts, examples and applications of quantum
(=non-commutative) probability will be presented.
Preliminaries would be a mild familiarity of random variables and
bounded linear operators on Hilbert spaces (or just matrices).