Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns. (1st August 2022)

• Record Type: Journal Article
• Authors: Fannjiang, Albert
• Is Part Of: Inverse problems. Volume 38:Number 8(2022)
• Publication Date: 2022-08-01
• Subjects: discrete tomography -- phase retrieval -- coded diffraction pattern -- uniqueness; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac77b0
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 3D tomographic phase retrieval under the Born approximation for discrete objects supported on a n × n × n grid is analyzed. It is proved that n projections are sufficient and necessary for unique determination by computed tomography with full projected field measurements and that n + 1 coded projected diffraction patterns are sufficient for unique determination, up to a global phase factor, in tomographic phase retrieval. Hence n + 1 is nearly, if not exactly, the minimum number of diffractions patterns needed for 3D tomographic phase retrieval under the Born approximation.