# Mathematics Colloquia and Seminars

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### Lattices from equiangular tight frames with applications to lattice sparse recovery

**PDE and Applied Math Seminar**

Speaker: | Deanna Needell, Claremont McKenna College |

Related Webpage: | http://www1.cmc.edu/pages/faculty/DNeedell/ |

Location: | 1147 MSB |

Start time: | Tue, Apr 18 2017, 4:10PM |

It is now well known that one can efficiently recover a sparse signal from a small number of linear measurements. However, typically one not only knows the signal has a sparse representation in some basis, but the signal may also possess some other type of structure. Model-based sparse recovery addresses additional structures like block sparsity, spread sparsity, or when the signal is known to reside in some other convex space. However, if the signal is also known to lie in some lattice, very little is known about how this additional structure can be successfully utilized. Motivated by this problem, we introduce some theory from Algebra and provide results describing when the set of integral linear combinations of atoms from an equiangular tight frame form a lattice. Such an understanding should lead to designs of sampling operators for sparse lattice signals. The talk concludes with open questions and future directions.

Nonstandard date for applied math/PDE seminar