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In this presentation, I will talk about two kinds of two applications: 3D localization of space debris and limited-angle computed tomography reconstruction. These seemingly unrelated topics are connected and addressed by sparse recovery approaches. In the first application, we consider the high-resolution imaging problem of 3-dimensional (3D) point source image recovery from 2-dimensional data using a method based on point spread function (PSF) engineering. A new non-convex regularization method with a data-fitting term based on Kullback--Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. Besides, we further study the 3D localization and material classification of unresolved space debris using a multispectral rotating PSF by proposing a three-stage algorithm scheme. In the second application, we consider minimizing the L1/L2 term on the gradient for a limited-angle scanning problem in computed tomography (CT) reconstruction. We design a specific splitting framework for an unconstrained optimization model so that the alternating direction method of multipliers (ADMM) has guaranteed convergence under certain conditions. At last, I will talk about the prospect of the on-going projects at UCD.

zoom info available https://sites.google.com/view/maddd After the talk, we will do virtual tea/coffee get-together at https://gather.town/KOoFj0aKT5GkEj40/Alder-Room