Well-conditioned ptychographic imaging via lost subspace completion. (25th September 2020)

• Record Type: Journal Article
• Authors: Forstner, Anton; Krahmer, Felix; Melnyk, Oleh; Sissouno, Nada
• Is Part Of: Inverse problems. Volume 36:Number 10(2020)
• Publication Date: 2020-09-25
• Subjects: phase retrieval -- ptychography -- regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abaf3a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such measurements is known to be an ill-posed problem. Although for some windows the conditioning can be controlled, for a number of important cases it is not possible, for instance for Gaussian windows. In this paper we develop a subspace completion algorithm, which enables stable reconstruction for a much wider choice of windows, including Gaussian windows. The combination with a regularization technique leads to improved conditioning and better noise robustness.