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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Mathematical model and stability analysis for an i
 nverse problem in light sheet fluorescence microsc
 opy - Matias Courdurier (Pontificia Universidad Ca
 tólica de Chile)
DTSTART;TZID=Europe/London:20230331T090000
DTEND;TZID=Europe/London:20230331T095000
UID:TALK198280AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198280
DESCRIPTION:In Fluorescence Microscopy\, a small and almost tr
 ansparent sample containing a distribution of fluo
 rophore is illuminated\, e.g. with a laser\, to ac
 tivate the fluorescence. A camera outside the samp
 le detects the activated fluorescence light and th
 e fluorophore distribution inside the sample is es
 timated from these exterior measurements. In Light
  Sheet Fluorescence Microscopy (LSFM)\, the strate
 gy is to optically section the sample by illuminat
 ing a single plane perpendicular to the camera at 
 a time\, which produces a good reconstruction of t
 he fluorophore distribution by direct imaging\, bu
 t blurring artifacts are observed on the fluoropho
 re reconstruction as you move further away from th
 e illumination side.\nThis motivated us to conside
 r a mathematical model for LSFM that includes a sm
 all diffusion effect in the illumination stage of 
 LSFM. In the model we considered\, the reconstruct
 ion of the fluorophore distribution can be recast 
 as a backwards heat equation inverse problem\, whe
 re the goal is to reconstruct the initial conditio
 n in the heat equation from measurements of the so
 lution in non-cylindrical space-time surface obser
 vation set.\nFor this specific family of backwards
  heat equation problems\, we obtain uniqueness and
  logarithmic stability results\, which then transl
 ate into corresponding uniqueness and stability re
 sults for the LSFM inverse problem of reconstructi
 ng the fluorophore distribution.\nThis is a joint 
 work with Pablo Arratia\, Victor Casta\\~neda\, Ev
 elyn Cueva\, Steffen H\\"artel\, Axel Osses and Be
 njamin Palacios.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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