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


Chao Wang, Postdoctoral Researcher
Wake Forest University and UT—Dallas

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

Abstract: We are concerned with the high-resolution imaging and localization problem of 3D point source image recovery from 2D data using methods based on point spread function (PSF) design. A new technique patented by S. Prasad for applying rotating point spread functions with a single lobe to obtain depth from defocus is considered. Applications include high-resolution single molecule localization microscopy, as well as localization of space debris using a space-based telescope. We develop and apply several recovery algorithms for this problem. Finding the locations and fluxes is a large-scale sparse 3D inverse problem. We have developed solution algorithms based on matching pursuit and non-convex optimization. In the matching pursuit case, we develop and apply a single best replacement (SBR) algorithm for our 3D localization problem. Acceleration techniques on searching processing and pre-computation are proposed. In the nonconvex optimization case, we consider two kinds of noise models. The continuous exact l 0 model (CEL0) with a least squares data-fitting term is applied for the Gaussian noise model, and a new nonconvex regularization method with data-fitting term based on Kullback-Leibler (KL) divergence is proposed for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms.

Tuesday, July 31, 2018 at 3:30 PM in Manchester Hall, Room 229