Learning Low-Dimensional Models of Microscopes

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.

Deepblur: Blind Identification Of Space Variant Psf

“…This methodology is robust in the sense that even if the neural network is trained on a set of natural images, it still performs well on biological images not seen during the training. We will extend this work to blur operators adapted to large images estimated from microscopes in [10]. We expect this approach to provide a turnkey tool for biologists to improve their image quality.…”

“…Assumption 1.1 is realistic in many microscopes. The space H can be estimated by imaging fluorescent micro-beads [10], or provided that we have access to a collection of operators [11]. Assumption 1.2 (A conical hull in H).…”

“…The subspace H and the convex set C are computed using the estimation procedure described in [10]. We use the operators described in Section 1.2.1.…”

Modelling a Microscope as Low Dimensional Subspace of Operators

“…• for a single operator, the bases (u i ) and (v j ) can be estimated efficiently by imaging sets of fluorescents beads as will be seen later [6], [8], [3].…”

“…The steps we propose are based on standard image processing tools: i) detection of potential PSFs by applying a Laplacian of Gaussian filter followed by a thresholding, ii) selection of patches containing a single maximum, iii) centering of the remaining patches by finding the best fit with a pyramid of Gaussian iv) discarding the likely outliers by performing specific z-tests among the patch population and v) resampling on a shifted grid using bi-cubic splines. We refer the interested reader to [3] for more details. As an output of this step, we have collected a (large) series of reliable PSF patches (p 1 , .…”