Chao Wang, Chinese University of Hong Kong (CUHK); Robert Plemmons, Wake Forest University; Sudhakar Prasad, University of New Mexico; Raymond Chan, Chinese University of Hong Kong (CUHK); Mila Nikolova, ENS Cachan, University of Paris-Saclay
Keywords: 3D localization, image rotation, space debris, sparsity based non-convex optimization algorithms, image processing
Abstract:
We consider 3D localization and tracking of space debris at optical wavelengths by using a space-based telescope, which is an important and challenging task in space surveillance. Image data taken with a specially designed point spread function (PSF) that encodes, via a simple rotation, changing source distance can be employed to acquire a three dimensional (3D) field of unresolved sources like space debris. A simple approach to effect such PSF rotation, which was originally proposed by Prasad [1] in 2013, utilizes an annular phase mask design of spiral phases with winding numbers that are regularly spaced from one annular zone to the next. Such a mask can be easily mounted on a telescope. When actively illuminated by a laser, unresolved space debris, which can be regarded as a swarm of point sources, can scatter a fraction of the laser irradiance back into the imaging sensor. The technique is well suited to optically localize small, sub-centimeter class space debris, at distances of hundreds of meters.
We discuss here the problem of 3D localization of closely spaced point sources from simulated noisy image data obtained by using such a rotating-PSF imager. The localization problem is discretized on a cubical lattice where the coordinates and values of its nonzero entries represent the 3D locations and fluxes of the sources, respectively. Finding the locations and fluxes of a few point sources on a large lattice is evidently a large-scale sparse 3D inverse problem. For the Gaussian and Poisson statistical noise models, we describe the results of simulation using novel non-convex sparse optimization algorithms to extract both the 3D location coordinates and fluxes of individual debris particles from noisy rotating-PSF imagery. For Gaussian noise, which describes conventional CCD sensors operating at low per-pixel photon fluxes and large read-out noise, a continuous exact L0 (CEL0) penalty term [2] added to a least-squares data fitting term constitutes an L0-sparsity non-convex optimization protocol with promising results. For the Poisson noise model, which characterizes an EMCCD sensor operated in the photon-counting (PC) regime, we show that an iteratively re-weighted L1 (IRL1) algorithm based on the sum of a Kullback-Leibler I-divergence data fitting term and a novel non-convex penalty term [3] performs well. Image data of the type we discuss here could be acquired by a combined active illumination – imaging system that can be mounted on a space asset in order to optically monitor its debris neighborhood. Further work involving snapshot multi-spectral imaging for material characterization, and higher 3D resolution and localization of space micro-debris via a sequence of snapshots is under way.
The authors acknowledge funding support for the work from the AFOSR under grant FA9550-15-1-0286, and from HKRGC Grant No. CUHK14306316, HKRGC CRF Grant C1007-15G, HKRGC AoE Grant AoE/M-05/12, CUHK DAG No. 4053211, and CUHK FIS Grant No. 1907303.
References
[1] S. Prasad, Rotating point spread function via pupil-phase engineering, Optics letters, vol. 38, no. 4, pp. 585587, 2013.
[2] E. Soubies, L. Blanc-F ?eraud, and G. Aubert, A continuous exact l0 penalty (CEL0) for least squares regularized problem, SIAM Journal on Imaging Sciences, vol. 8, no. 3, pp. 16071639, 2015.
[3] C. Wang, R. Chan, M. Nikolova, R. Plemmons, and S. Prasad, Nonconvex optimization for 3D point source localization using a rotating point spread function, arXiv preprint: 1804.04000, 2018.
Date of Conference: September 11-14, 2018
Track: Poster