# MS-3 Compressed sensing and matrix completion (Compressed Sensing)

### Organizers: Simon Foucart (Texas A&M University) and Namrata Vaswani (Iowa State University)

Compressed Sensing has recently had a tremendous impact in science and engineering, because it revealed the theoretical possibility of acquiring structured high-dimensional objects using much less information than previously expected, and because it also provided practical procedures to perform the reconstruction based on the limited information available. The foundations of the field rely on an elegant mathematical theory with linear algebra at its core. The standard compressed sensing problem consists in solving underdetermined linear systems whose solutions are known to possess an a priori structure such as sparsity. There are several extensions of the standard problem, e.g. when sparse vectors are replaced by low-rank matrices which must be completed from the knowledge of only a few of their entries. A motivating application is found in the Netflix problem, where the matrix of movie ratings has to be reconstructed based on only a few ratings by each user. The goal of the mini-symposium is to highlight interplays between mathematics in general, and linear algebra in particular, with other fields (engineering, computer science, and statistics) that have shaped the theory of compressive sensing and low-rank matrix recovery.

### Speakers

**Waheed Bajwa**, *Collaborative dictionary learning from big, distributed data*

**Yuxin Chen**, *The Projected Power Method: A Nonconvex Algorithm for Joint Alignment*

**Yuejie Chi**, *Provably robust and fast low-rank matrix recovery with outliers*

**Simon Foucart**, *Concave Mirsky Inequality and Low-Rank Recovery*

**Paul Hand**, *Compressed Sensing from Phaseless Gaussian Measurements via Linear Programming in the Natural Parameter Space*

**Chinmay Hegde**, *Stable inversion of (certain) random periodic feature maps*

**Arian Maleki**, *On The Asymptotic Performance of ℓ _{q}-regularized Least Squares*

**Hassan Mansour**, *A Kaczmarz Method for Low Rank Matrix Recovery*

**Dustin Mixon**, *Explicit Restricted Isometries*

**Rob Nowak**, *Low Rank Matrix Completion and Beyond*

**Rayan Saab**, *Phase retrieval from local measurements*

**Ludwig Schmidt**, *Faster Constrained Optimization via Approximate Projections*

**Namrata Vaswani**, *New Results for Provably Correct Dynamic Robust Principal Components Analysis (PCA)*