Justin Romberg教授将在他访问清华大学期间就压缩感知领域的学术前沿及其课题组的最新研究成果做一场讲座。

## 讲座题目

Using structure to solve underdetermined systems of linear equations and overdetermined systems of quadratic equations

## 讲座时间

10:00 - 11:00, October 14th

## 讲座地点

清华大学罗姆楼3层报告厅

## 讲座内容

We will start by giving a highlevel overview of the fundamental results in the field that has come to be known as compressive sensing. The central theme of this body of work is that underdetermined systems of linear equations can be meaningfully "inverted" if they have structured solutions. Two examples of structure would be if theunknown entity is a vector which is sparse (has only a few "active" entries) or if it is a matrix which is low rank. We discuss some of the applications of this theory in signal processing and statistics.

In the second part of the talk, we will show how some of these structured recovery results give us new insightinto solving systems of quadratic and bilinear equations. In particular, we consider the general problem of blind deconvolution: we observe the convolution of two vectors, and show how making some mild structural assumptions about these signals allows us to recover them by solving a convex program.