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SUMMARY:Learning under group actions: The sample complexity of Multi-refer
 ence Alignment
DTSTART:20170620T100000
DTEND:20170620T110000
DTSTAMP:20260406T190058Z
UID:d83472977285f39fb5829f46fd9ce5d128fee9c74a2313f538f54d92
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Afonso S. Bandeira\, NYU\nMany problems in signal/image 
 processing\, and computer vision amount to estimating a signal\, image\, o
 r tri-dimensional structure/scene from corrupted measurements. A particula
 rly challenging form of measurement corruption are latent transformations 
 of the underlying signal to be recovered. Examples include the Simulatenou
 s Localization and Mapping (SLaM) problem in Robotics and Computer Vision\
 , where pictures of a scene are obtained from different positions and orie
 ntations\, Cryo-Electron Microscopy (Cryo-EM) imaging where projections of
  a molecule density are taken from unknown rotations\, and several others.
 \n\nOne fundamental example of this type of problems is Multi-reference Al
 ignment: in one of its simplest forms the goal is to estimate a signal fro
 m noisy cyclically shifted copies. We will show that the number of observa
 tions needed has a surprising dependency on the signal-to-noise ratio (SNR
 )\, and algebraic properties of the underlying group action. Remarkably\, 
 in some important cases\, this sample complexity is achieved with computat
 ionally efficient methods based on computing invarants under the group of 
 transformations.\n\nWe will also discuss the sample complexity of the hete
 rogeneous multi-reference alignment problem where the samples come from a 
 mixture of signals\, and provide the first known procedure that provably a
 chieves signal recovery in the low SNR regime. A related problem is hetero
 genous reconstruction in Cryo-Electron Microscopy (Cryo-EM) imaging where 
 multiple unknown molecules or molecules in multiple unknowm conformations 
 are imaged together. Our work can be seen as a first step towards a comple
 te statistical theory of heterogenous Cryo-EM.
LOCATION:INR 113
STATUS:CONFIRMED
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