Title: The Power of Structured Sparsity in Data Acquisition and Inference
Speaker: Chinmay Hegde, Postdoctoral Associate, Massachusetts Institute of Technology
Abstract: Sparse representations for data have emerged as powerful tools in signal processing, statistics, and machine learning. However, signals and images encountered in practice often exhibit rich structure beyond mere sparsity alone. As one example, the dominant wavelet coefficients of natural images can be organized in the form of a connected tree. As another example, the nonzero pixels of a high-resolution image of the night sky occur as contiguous clusters. How do we leverage these notions of structure in large-scale data processing applications?
In this talk, I will describe a general framework to capture secondary structure in sparse signals and images. The key idea lies in developing concise signal models for structured sparsity that exploit the inter-dependencies between values and locations of the signal coefficients. I will discuss numerical techniques for constructing corresponding algorithms (with provable guarantees) for these new models. These techniques rely heavily on ideas from discrete optimization and are fundamentally non-convex. Despite these feature, I will show that the methods enjoy a (nearly) linear-time complexity, ensuring that they easily scale to massive datasets.
I will discuss the impact of structured sparsity models in data acquisition and inference applications. In particular, I will show that my methods enable algorithms for: (i) sample-optimal compressive sensing of natural image classes; and (ii) robust feature identification in large-scale images of the earth’s subsurface encountered in exploration geophysics.
Speaker Bio: Chinmay Hegde joined the Theory of Computation (ToC) group at MIT in October 2012, where he is currently a Shell-MIT postdoctoral research associate. Prior to this, he received the B.Tech. degree in Electrical Engineering from IIT Madras (India), and the M.S. and Ph.D. degrees in Electrical and Computer Engineering from Rice University. Dr. Hegde is the recipient of the best student paper award in SPARS 2009, the Robert Patton award for university service in 2010, and the Ralph Budd award for best engineering thesis in Rice University in 2013. His research interests include signal and image processing, algorithm design, and machine learning.