Compressive sensing (CS) is new method for sensing and signal recovery from far-fewer measurements than what is suggested by traditional sampling theories. This has immense benefits in applications where we seek to sense at faster speeds, higher resolution, lower power consumption and reduced sensor costs. At the heart of CS is the idea that we can solve under-determined linear systems using sparse signal representations and specialized convex optimization techniques.

In this course, we will develop a formal study of techniques required to solve under-determined linear systems. We will discuss the theory and practice of sparse optimization. This will involve a rich interplay of ideas from linear algebra, probability, and convex optimization. Finally, we will explore broader applications in computational imaging, neural signal processing, and sparse regression that benefit from the theory and optimization methods developed in the course.

Course goals: 1) A formal understanding of theory and optimization techniques required to solver under-determined linear systems. 2) Understand practical implications of signal processing with non-linear models.

Pre-requisites: Undergraduate linear algebra, probability and signal processing.