C. Hébert

Nathanaël Perraudin, Adrien Teutrie, Cécile Hébert et al.

We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds significant relevance in numerous Machine Learning applications, particularly within the domain of physical linear unmixing problems. A notable challenge arises from the main loss term in the Poisson NMF problem being a KL divergence, which is non-Lipschitz, rendering traditional gradient descent-based approaches inefficient. In this contribution, we explore the utilization of Block Successive Upper Minimization (BSUM) to overcome this challenge. We build approriate majorizing function for Lipschitz and relatively smooth functions, and show how to introduce linear constraints into the problem. This results in the development of two novel algorithms for regularized Poisson NMF. We conduct numerical simulations to showcase the effectiveness of our approach.

Okan Altingövde, Anastasiia Mishchuk, Gulnaz Ganeeva et al.

Curvilinear structures frequently appear in microscopy imaging as the object of interest. Crystallographic defects, i.e., dislocations, are one of the curvilinear structures that have been repeatedly investigated under transmission electron microscopy (TEM) and their 3D structural information is of great importance for understanding the properties of materials. 3D information of dislocations is often obtained by tomography which is a cumbersome process since it is required to acquire many images with different tilt angles and similar imaging conditions. Although, alternative stereoscopy methods lower the number of required images to two, they still require human intervention and shape priors for accurate 3D estimation. We propose a fully automated pipeline for both detection and matching of curvilinear structures in stereo pairs by utilizing deep convolutional neural networks (CNNs) without making any prior assumption on 3D shapes. In this work, we mainly focus on 3D reconstruction of dislocations from stereo pairs of TEM images.