Algorithms for large-scale sparse reconstruction

Many signal processing applications seek to approximate a signal as a linear combination of only a few elementary atoms drawn from a large collection. This is known as sparse reconstruction, and the theory of compressed sensing allows us to pose it as a structured convex optimization problem. I will discuss the role of duality in revealing some unexpected and useful properties of these problems, and will show how they can lead to practical, large-scale algorithms. I will also describe some applications of these algorithms.