title: Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing.
abstract: We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.
authors.affiliation: Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China. sunmingjian@hit.edu.cn
authors.forename: Yoav
authors.initials: Y
authors.lastname: Shechtman
authors.forename: Yonina C
authors.initials: YC
authors.lastname: Eldar
authors.forename: Alexander
authors.initials: A
authors.lastname: Szameit
authors.forename: Mordechai
authors.initials: M
authors.lastname: Segev
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D044962:Data Compression / Q000379:methods*; D003952:Diagnostic Imaging / Q000379:methods; D004867:Equipment Design; D005583:Fourier Analysis; D008027:Light; D008853:Microscopy / Q000379:methods*; D015233:Models, Statistical; D016011:Normal Distribution; D055095:Optics and Photonics / Q000379:methods