Sparsity-enforcing optimization for 3D single-molecule localisation in genomic imaging

In recent years, advances in genomic imaging have enabled the study of the 3D organization of chromosomes within the cell nucleus. Among the techniques developed for this purpose, Oligopaints-based Stochastic Optical Reconstruction Microscopy (STORM) enables the acquisition of high-resolution images of specific genomic regions, which can be used to trace chromatin paths. These images can be used for Volumetric Chromatin Tracing, a technique that preserves the 3D topographical arrangement of genomic loci. This approach requires acquiring thousands of images per genomic region, followed by the detection and localization of active fluorophores whose positions are used to reconstruct chromatin structure. Accurate chromatin tracing, therefore, depends on localization algorithms capable of identifying emitters with nanometric precision, which remains a technically challenging task. This thesis focuses on the mathematical modeling and algorithmic development for three-dimensional single-molecule localization in STORM imaging. A forward mathematical model of the STORM image acquisition process is introduced, and based on this model, a simulator for STORM images is implemented to generate synthetic datasets for numerical experiments. Furthermore, the localization problem is formulated as a regularized inverse problem, incorporating sparsity-promoting regularization to recover the 3D coordinates of emitters from STORM images. Numerical methods are implemented and evaluated, and their performance is compared with existing single-molecule localization approaches, like ThunderSTORM.