Richard Baraniuk (joint with Chinmay Hegde, Marco Duarte, Mark Davenport, Michael Wakin)

Title: Compressive Learning and Inference

Abstract: Compressive Sensing (CS) is a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via measurements using more general, even random, test functions. In contrast with conventional wisdom, the new theory asserts that one can combine "low-rate sampling" with an optimization-based reconstruction process for efficient and accurate signal acquisition.  While the growing CS literature has focused on reconstructing signals, in many applications, we are ultimately interested only in making inferences about the data.  Examples include detecting tumors in medical images, classifying the type of vehicle in airborne surveillance, or estimating the trajectory of an object in a video sequence.  In this talk we will review our recent work on new algorithms for compressive learning and inference that enjoy the same general benefits as CS.  Specific techniques include compressive versions of the matched filter (dubbed the "smashed filter"), intrinsic dimension estimation for point clouds, and manifold learning algorithms.  In our techniques, the number of measurements required is linear in the complexity of the data (sparsity in the case of a basis representation or dimension in the case of a manifold model) and only logarithmic in the ambient dimension.