in collaboration with

- Penghuan Liu, Sébastien Bourguignon, LS2N, Nantes

- Simon Labouesse, Marc Allain, Anne Sentenac, Institut Fresnel, Marseille

For most active wave imaging systems, the recorded data are related to the observed scene via a simple convolution with a point-spread function (PSF). Because of fundamental diffraction limits, the Fourier transform of the PSF has a bounded support that ultimately limits the resolution of the imaging system. Thanks to controlled nonuniform illumination patterns, advanced imaging systems such as Structured Illumination Microscopes (SIM) produce a super-resolution (SR) effect of a factor 2 by shifting high-frequency components of the object into the spatial baseband. However, SIM microscopes are complex and expensive, because the illumination patterns need to be strictly controlled. Several recent papers propose simpler acquisition systems called Blind-SIM, where the illuminations become unknowns.

The presentation provides a first mathematical understanding of the SR capacity of Blind-SIM, when the illumination is a speckle noise. We obtain the somewhat surprising result that the SR ratio remains the same, the illumination pattern being known or unknown. This property can be achieved by taking advantage of the second-order statistical information of the acquired images.

In a second part, we focus on the computational aspects of the problem. A first minimal contrast method is proposed, which confirms that blind-SIM can reach an SR ratio equal to 2. However, the computing cost is very high and does not scale to realistic size problems. We finally propose a more efficient variant, which neglects some of the long-range correlations.