This course will provide students with theoretical and practical knowledge of a new and stimulating research area, namely compressed sensing. This topic was initially driven by imaging applications, but is appealing for many areas of engineering and mathematics, due to the extremely large number and type of possible applications.
This course covers the topic of compressed sensing, an innovative signal sensing and representation paradigm that is significantly more efficient than conventional sampling as described by Shannon’s theorem. Compressed sensing represents a signal through a small set of linear projections of the signal samples; the original samples can be reconstructed via a nonlinear process. This very compact representation has many potential advantages in the areas of signal acquisition and communication, as well as visual information processing. The course will address the theory of compressed sensing and its practical applications. It will involve 15 hours, divided into 12 hours of lectures and 3 hours of computer labs using Matlab, where the students will become familiar with compressed sensing algorithms using a hands-on approach. The lectures will cover both theory and applications. The course will start with the introduction of the mathematical aspects of compressed sensing, including deterministic reconstruction conditions, the restricted isometry property, and reconstruction algorithms such as basis pursuit, orthogonal matching pursuit, and iterative thresholding. After that, the course will address a few key applications of compressed sensing, with particular regard to communications, applications to visual signals, and implementation aspects.