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Sparse Recovery Algorithms for 3D Imaging using Point Spread Function Engineering

Presented by: 
Robert Plemmons
Friday 3rd November 2017 - 14:00 to 14:50
INI Seminar Room 1
Co-authors: Chao Wang (Mathematics, Chinese University of Hong Kong), Raymond Chan (Mathematics, Chinese University of Hong Kong), Sudhakar Prasad (Physics, University of New Mexico)

Imaging and localizing point sources with high accuracy in a 3D volume is an important but challenging task. For example, super-resolution 3D single molecule localization is an area of intense interest in biology (cell imaging, folding, membrane behavior, etc.), in chemistry (spectral diffusion, molecular distortions, etc.), and in physics (structures of materials, quantum optics, etc.). We consider here the high-resolution imaging problem of 3D point source image recovery from 2D data using methods based on point spread function (PSF) design. The methods involve a new technique, recently patented by S. Prasad, for applying rotating point spread functions with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. The distribution of point sources is discretized on a cubical lattice where the indexes of nonzero entries represent the 3D locations of point sources. The values of these entries are the point source fluxes. Finding the locations and fluxes is a large-scale sparse 3D inverse problem and we have developed solution algorithms based on sparse recovery using non-convex optimization. Applications to high-resolution single molecule localization microscopy are described, as well as localization of space debris using a space-based telescope. Sparse recovery optimization methods, including the Continuous Exact L0 (CEL0) algorithm, are used in our numerical experiments.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons