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UID:1831-1580818500-1580821800@colleges.claremont.edu
SUMMARY:Covering point-sets with parallel hyperplanes and sparse signal recovery (Lenny Fukshansky\, CMC)
DESCRIPTION:Let S be a set of k > n points in n-dimensional Euclidean space. How many parallel hyperplanes are needed to cover it? In fact\, it is easy to prove that every such set can be covered by k-n+1 parallel hyperplanes\, but do there exist sets that cannot be covered by fewer parallel hyperplanes? We construct a family of examples of such extremal sets. We then use it\, along with a result on girth of bipartite graphs\, to construct a family of n x d integer matrices with bounded sup-norm and the property that no m column vectors are linearly dependent\, m < n. If m < (log n)^{1-e} for any e > 0\, then d/n tends to infinity as n tends to infinity. This is a deterministic construction of a family of sensing matrices\, which are used for sparse signal recovery in compressed sensing. Joint work with Alex Hsu.
URL:https://colleges.claremont.edu/ccms/event/covering-point-sets-with-parallel-hyperplanes-and-sparse-signal-recovery-lenny-fukshansky-cmc/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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