CSE 709: Compressed Sensing and Group Testing, Part I (Fall 2011 Seminar)

Brief Course Description

This is a year-long seminar on the general topic of sparse approximation, focusing on two central models of sparse approximation: combinatorial group testing, and compressive sensing. The topics are chosen partly to fit the (research) interests of the instructors.

1. (Fall 2011) Combinatorial group testing and applications. The basic setting of the group testing problem is to identify a subset of "positive" items from a huge item population using as few "tests" as possible. The meaning of "positive", "tests" and "items" are dependent on the application. For example, dated back to World War II when the area of group testing started, "items" are blood samples, "positive" means syphilis-positive, and a "test" contains a pool of blood samples which result in a positive outcome if there is at least one sample in the pool positive for syphylis. This basic problem paradigm has found numerous applications in biology, cryptography, networking, signal processing, coding theory, statistical learning theory, data streaming, etc. In this semester we introduce group testing from a computational view point, where not only the constructions of group testing strategies are of interest, but also the computational efficiency of both the construction and the decoding procedures are studied. We will also briefly introduce the probabilistic method, algorithmic coding theory, and several direct applications of group testing. We will also cover variations of group testing and their applications. The techniques we cover here will also be useful in compressive sensing which is covered in the next seminar.
2. (Spring 2012) Compressive sensing is based on the idea that many signals can be represented with only a few non-zero coefficients (under a suitably chosen basis). These signals can be "measured" using relatively few linear measurements and can be reconstructed from the measurement vectors efficiently. This paradigm has found numerous applications in signal processing, data streaming, image processing, and so forth. In this part of the seminar we shall cover the basics of compressive sensing, from efficient measurement matrix constructions to efficient signal reconstruction. Lowerbounds with interesting connections to communications complexity are also covered.