BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Plamen Stefanov (Purdue University)
DTSTART:20200604T160000Z
DTEND:20200604T170000Z
DTSTAMP:20260423T052502Z
UID:Inverse/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/3/">
 Noise in linear inverse problems</a>\nby Plamen Stefanov (Purdue Universit
 y) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\
 nAbstract\nWe study how noise in the data affects the noise in the reconst
 ruction\, for linear inverse problems\, more precisely when the operator w
 e have to invert is a Fourier Integral Operator. We apply the results to t
 he Radon transform in the plane in parallel and in fan-bean coordinates. I
 n this talk\, we concentrate on additive noise\, assuming that it is white
  but the methods apply to non-white noise as well.  We propose the microlo
 cal defect measure as a measure of the spectral power of the noise in the 
 phase space. We show that one can compute the spectral power of the noise 
 in the reconstruction\, including its standard deviation\, as a function o
 f the known statistical characteristics of the input noise. For the Radon 
 transform in parallel geometry\, we show that the induced noise is positio
 n independent\, isotropic\, and “blue”. In fan-bean coordinates\, the 
 noise varies with position and it is not isotropic anymore but still “bl
 ue”. This dependence is weak however and the standard deviation which we
  compute\, still gives a good characterization of the strength of the indu
 ced noise.\n \nThis is a joint project\, still in progress\, with Samy Tin
 del\, Purdue.\n
LOCATION:https://researchseminars.org/talk/Inverse/3/
END:VEVENT
END:VCALENDAR