Enhancing 3-D Cell Structures in Confocal and STED Microscopy: A Joint Model for Interpolation, Deblurring and Anisotropic Smoothing
Modern 3-D confocal and STED microscopes are especially suitable to investigate small detailed structures such as the filament network of a cell. In this talk, we present an advanced image enhancement method that copes with the typical limitations of these microscopy techniques: Low axial resolutions, Poisson noise and out-of-focus blur. More specifically, we introduce a joint model that unifies the tasks of denoising, deblurring and interpolation. Starting with a basic variational image restoration and inpainting functional, we propose its combination with a robust and regularised version of the famous Richardson-Lucy deconvolution. To enhance the One-dimensional tube-like structures of cell filaments, we replace the scalar-valued diffusivity in the associated partial differential equation (PDE) by a tensor valued one, leading to an anisotropic diffusion process. To solve the resulting PDE, we present a novel semi-implicit iteration scheme that increases both effciency and stability. Experiments on real-world data sets demonstrate a superior reconstruction quality of the recorded cells.