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In applications ranging from communications and image processing to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active must be learned from measurements. We derive universal bounds for the number of Gaussian measurements needed for signal recovery, which can then be extended to include subgaussian measurement schemes. The bound is universal in the sense that it only depends on the number of subspaces under consideration, and their orientation relative to each other. The particulars of the subspaces (e.g., compositions, overlaps, etc.) does not affect the results we obtain.As a special case, we derive sample bounds for the group lasso with overlapping groups.
Zach’s Abstract
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Without any prior preparation, and under extreme time limitations, can a team of researchers identify an interesting research problem, propose a novel solution, and submit a paper to a leading conference? This talk answers this question in the affirmative. We propose a high-throughput screening method for the detection of radioactive contraband. In the era of the dirty bomb, and under the looming scare of a nuclear Iran, our method may prove vital in securing our nation’s borders. Our solution is based on a convex relaxation of the generalized likelihood ratio test. This relaxation allows for efficient computation and can be extended to sequential tests that request additional data to resolve potential ambiguity if the available data is insufficient to reach a decision with high confidence. We model our observations using an inhomogenous Poisson process, hence our framework may also be useful for finding anomalous behavior in packet switching networks as well as the efficient detection of tumors in medical imaging.
Discovery Building, Orchard View Room
Nikhil Rao, Zachary Harmany