Labeling and denoising geometrically parameterized data with applications to Cryo-EM
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Many data sets encountered in practice depend continuously on a geometric parameter. An important example of this is image collections from Cryo-EM experiments, where the images depend continuously on the orientation of molecules. The first part of the thesis considers the problem of labeling geometrically parameterized data sets. It shows that for this problem the popular method of spectral clustering is sensitive to noise. It then presents a categorical optimization solution which is unbiased and robust to noise. The second part of the thesis presents a method to denoise collections of Cryo-EM images. The method represents Cryo-EM image collections as a single vector in a high dimensional space, and computes a low dimensional subspace which well contains the signal of the vector. By projecting the vector of images onto this subspace, the image collection is denoised. The thesis shows that the output images are centered, and that their SNR grows linearly with the number of input images.