ENGS 109 - High-dimensional Sensing and Learning (HdSL)


Sparsity has become a very important concept in recent years in applied mathematics, signal and image processing, and machine learning. The key idea is that many classes of natural signals can be described by only a small number of significant degrees of freedom. This course offers a complete coverage of the recently-emerged field of compressed sensing, which asserts that, if the true signal is sparse to begin with, accurate, robust, and even perfect signal recovery can be achieved from just a few randomized measurements. The course will then proceed to explore how and why this key concept of sparsity may play an important role in sampling theory and learning theory and be applied to a wide variety of real-world applications such as hyper-spectral imaging, cognitive radio, MRI, speech recognition, etc. The focus is on describing the novel ideas that have emerged in sparse recovery with emphasis on theoretical foundations, practical numerical algorithms, and various related signal processing applications. Students from diverse background (engineering, medicine, mathematics, etc.) who are either interested in the subject or want to apply this new theory for their research are encouraged to attend.


(MATH 8 or MATH 9) or (MATH 22 or MATH 24); MATH 20 is a plus; some proficiency of programing language (ENGS 20 or COSC 10)