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.