On the super-resolution capacity of imagers using unknown speckle illuminations

• Published in: IEEE transactions on computational imaging Vol. 4; no. 1; pp. 87 - 98
• Main Authors: Idier, Jérôme, Labouesse, Simon, Allain, Marc, Liu, Penghuan, Bourguignon, Sébastien, Sentenac, Anne
• Format: Journal Article
• Language: English
• Published: IEEE 01-01-2018
• Subjects: Computer Science; Signal and Image Processing; High-resolution; Optical microscopy; Photoacoustic imaging; Cutoff frequency; Multi-illumination imaging; Second-order statistics; Synthetic aperture radar
• ISSN: 2333-9403
• DOI: 10.1109/TCI.2017.2771729

Speckle-based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context, where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample. We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.