Fast and robust single particle reconstruction in 3D fluorescence microscopy

Single particle reconstruction has recently emerged in 3D fluorescence microscopy as a powerful technique to improve the axial resolution and the degree of fluorescent labeling. It is based on the reconstruction of an average volume of a biological particle from the acquisition multiple views with unknown poses. Current methods are limited either by template bias, restriction to 2D data, high computational cost or a lack of robustness to low fluorescent labeling. In this work, we propose a single particle reconstruction method dedicated to convolutional models in 3D fluorescence microscopy that overcome these issues. We address the joint reconstruction and estimation of the poses of the particles, which translates into a challenging non-convex optimization problem. Our approach is based on a multilevel reformulation of this problem, and the development of efficient optimization techniques at each level. We demonstrate on synthetic data that our method outperforms the standard approaches in terms of resolution and reconstruction error, while achieving a low computational cost. We also perform successful reconstruction on real datasets of centrioles to show the potential of our method in concrete applications.

Multiview point cloud registration with anisotropic and space-varying localization noise

In this paper, we address the problem of registering multiple point clouds corrupted with high anisotropic localization noise. Our approach follows the widely used framework of Gaussian mixture model (GMM) reconstruction with an expectation-maximization (EM) algorithm. Existing methods are based on an implicit assumption of space-invariant isotropic Gaussian noise. However, this assumption is violated in practice in applications such as single molecule localization microscopy (SMLM). To address this issue, we propose to introduce an explicit localization noise model that decouples shape modeling with the GMM from noise handling. We design a stochastic EM algorithm that considers noise-free data as a latent variable, with closed-form solutions at each EM step. The first advantage of our approach is to handle space-variant and anisotropic Gaussian noise with arbitrary covariances. The second advantage is to leverage the explicit noise model to impose prior knowledge about the noise that may be available from physical sensors. We show on various simulated data that our noise handling strategy improves significantly the robustness to high levels of anisotropic noise. We also demonstrate the performance of our method on real SMLM data.