No abstract

We propose accurate and computationally efficient procedures to calibrate fluorescence microscopes from microbeads images. The designed algorithms present many original features. First, they allow to estimate space-varying blurs, which is a critical feature for large fields of views. Second, we propose a novel approach for calibration: instead of describing an optical system through a single operator, we suggest to vary the imaging conditions (temperature, focus, active elements) to get indirect observations of its different states. Our algorithms then allow to represent the microscope responses as a lowdimensional convex set of operators. This approach is deemed as an essential step towards the effective resolution of blind inverse problems. We illustrate the potential of the methodology by designing a procedure for blind image deblurring of point sources and show a massive improvement compared to alternative deblurring approaches both on synthetic and real data.

We propose a scalable method to find a subspace H of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of the Tucker-2 decomposition model, which was never used in this context. In addition, we propose to construct a convex set C ⊂ H as the convex hull of the observed operators. It is a minimax optimal estimator under the Nikodym metric. We then provide an efficient algorithm to compute projection on C. We observe a good empirical behavior of the method in simulations. The main aim of this work is to improve the identifiability of complex linear operators in blind inverse problems.

Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a discrete measure containing a few isolated Dirac masses at an unknown location. Is this information enough to recover the impulse response location and the operator with a sub-pixel accuracy? We study this question and bring to light key geometrical quantities for exact and stable recovery. We also propose an in-depth study of the presence of additive white Gaussian noise. We illustrate the well-foundedness of this theory on the challenging optical imaging problem of blind deconvolution and blind deblurring with non-stationary operators.

We propose to train a neural network to estimate space varying blur operators from a single blurry image. The key assumption is that the operator lives in a subset of a known subspace, which is a reasonable assumption in many microscopes. We detail a specific sampling procedure of the subset to train a Resnet architecture. This allows a fast estimation. We finally illustrate the performance of the network on deblurring problems.