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SUMMARY:Mathematical model and stability analysis for an inverse problem i
 n light sheet fluorescence microscopy - Matias Courdurier (Pontificia Univ
 ersidad Católica de Chile)
DTSTART:20230331T080000Z
DTEND:20230331T085000Z
UID:TALK198280@talks.cam.ac.uk
DESCRIPTION:In Fluorescence Microscopy\, a small and almost transparent sa
 mple containing a distribution of fluorophore is illuminated\, e.g. with a
  laser\, to activate the fluorescence. A camera outside the sample detects
  the activated fluorescence light and the fluorophore distribution inside 
 the sample is estimated from these exterior measurements. In Light Sheet F
 luorescence Microscopy (LSFM)\, the strategy is to optically section the s
 ample by illuminating a single plane perpendicular to the camera at a time
 \, which produces a good reconstruction of the fluorophore distribution by
  direct imaging\, but blurring artifacts are observed on the fluorophore r
 econstruction as you move further away from the illumination side.\nThis m
 otivated us to consider a mathematical model for LSFM that includes a smal
 l diffusion effect in the illumination stage of LSFM. In the model we cons
 idered\, the reconstruction of the fluorophore distribution can be recast 
 as a backwards heat equation inverse problem\, where the goal is to recons
 truct the initial condition in the heat equation from measurements of the 
 solution in non-cylindrical space-time surface observation set.\nFor this 
 specific family of backwards heat equation problems\, we obtain uniqueness
  and logarithmic stability results\, which then translate into correspondi
 ng uniqueness and stability results for the LSFM inverse problem of recons
 tructing the fluorophore distribution.\nThis is a joint work with Pablo Ar
 ratia\, Victor Casta\\~neda\, Evelyn Cueva\, Steffen H\\"artel\, Axel Osse
 s and Benjamin Palacios.
LOCATION:Seminar Room 1\, Newton Institute
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