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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Recovery conditions of compressed sensing approach
to uncertainty quantification - Hoang Tran (Oak
Ridge National Laboratory)
DTSTART;TZID=Europe/London:20180206T090000
DTEND;TZID=Europe/London:20180206T100000
UID:TALK99931AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/99931
DESCRIPTION:Co-author: Clayton Webster (UTK/ORNL). This talk
is concerned with the compressed sensing approach
to reconstruction of high-dimensional functions fr
om limited amount of data. In this approach\, the
uniform bounds of the underlying global polynomial
bases have often been relied on for the complexit
y analysis and algorithm development. We prove a n
ew\, improved recovery condition without using thi
s uniform boundedness assumption\, applicable to m
ultidimensional Legendre approximations. Specifica
lly\, our sample complexity is established using t
he unbounded envelope of all polynomials\, thus in
dependent of polynomial subspaces. Some consequent
\, simple criteria for choosing good random sample
sets will also be discussed. In the second part
\, I will discuss the recovery guarantees of nonco
nvex optimizations. These minimizations are genera
lly closer to l_0 penalty than l_1 norm\, thus it
is widely accepted (also demonstrated computationa
lly in UQ) that they are able to enhance the spars
ity and accuracy of the approximations. However\,
the theory proving that nonconvex penalties are as
good as or better than l1 minimization in sparse
reconstruction has not been available beyond a few
specific cases. We aim to fill this gap by establ
ishing new recovery guarantees through unified nul
l space properties that encompass most of the curr
ently proposed nonconvex functionals in the litera
ture\, verifying that they are truly superior to l
_1.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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