BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexei Novikov (Penn State University) DTSTART:20210527T160000Z DTEND:20210527T170000Z DTSTAMP:20260423T035609Z UID:Inverse/48 DESCRIPTION:Title: Imaging with highly incomplete and corrupted data\nby Alexei Novikov (Penn State University) as part of International Zoom Inverse Problems Sem inar\, UC Irvine\n\n\nAbstract\nWe consider the problem of imaging sparse scenes from a few noisy data using an l1-minimization approach. This probl em can be cast as a linear system of the form Ax=b. The dimension of the u nknown sparse vector x is much larger than the dimension of the data vecto r b. The l1-minimization alone\, however\, is not robust for imaging with noisy data. To improve its performance we propose to solve instead the aug mented linear system [A|C]x=b\, where the matrix C is a noise collector. I t is constructed so as its column vectors provide a frame on which the noi se of the data can be well approximated with high probability. This approa ch gives rise to a new hyper-parameter free imaging method that has a zer o false discovery rate for any level of noise. We further apply the idea o f the noise collector to signal recovery from cross-correlated data matrix bb’. Cross-correlations naturally arise in many fields of imaging\, suc h as optics\, holography and seismic interferometry. The unknown is now a matrix xx’ formed by the cross correlation of the unknown signal. Henc e\, the bottleneck for inversion is the number of unknowns that grows quad ratically with dimension of x. The noise collector helps to reduce the dim ensionality of the problem by recovering only the diagonal of xx’\, whos e dimension grows linearly with the size of x. I will demonstrate the effe ctiveness of our approach for radar imaging. The method itself\, however\, can be applied in\, among others\, medical imaging\, structural biology\, geophysics and high-dimensional linear regression in statistics. This is a joint work with M. Moscoso\, G.Papanicolaou and C. Tsogka.\n LOCATION:https://researchseminars.org/talk/Inverse/48/ END:VEVENT END:VCALENDAR