Graduate Student Seminar: Alignment in Multireference alignment: is all hope lost or is it all model bias? Speaker: João Pereira

In the multireference alignment (MRA) model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. If the circular translations were known, the natural solution would be to average the observations after rotating them back, so one approach to MRA would be determining the circular shifts; this technique is known as alignment. In previous talks about MRA, I mentioned alignment did not work in the low signal to noise regime, but this might not be entirely true. In this informal talk, I'll talk about how we can use alignment to extract the phase from the original signal, and then fill out the magnitude of the signal using the method of moments. However depending on the choice of the first template for alignment, the solution given by alignment might start to resemble more the chosen template than the original signal from where the observations originate; this is known as model bias. As an illustration of this phenomenon, I'll show what happens if we align a great number of images of white gaussian noise with Einstein's picture, and then average them.

Joint work with Afonso Bandeira, Amit Singer and Andy Zhu.