Jonathan Fransson: Total Variation-regularization in fluorescence microscopy

Since a few years back, there has been a development boom of nano-scale imaging of cells and sub-cellullar structures. In short, the technique consists of making the specimen under study self-luminous when radiated by a laser of a fixed wavelength. Now, higher radiation intensity results in a higher signal to noise ratio, which gives a higher quality image with finer details. The backside is the damaging of the object when radiated with high intensity laser. Especially for the case of imaging live cells, one is interested in doing as little damage as possible. As a consequence, the image result becomes noisy. Retrieving data information from a noisy signal is a mathematical problem (inverse problem). This thesis focuses on developing a software for reconstructing noisy confocal images, utilizing the mathematical theory of regularization. More specifically, the reconstruction is based on total variation regularization and its extension, Bregman iterations. The presentation will present some performance results of the applied software and also investigate how the regularization method depends on the choice of regularization parameter for different noise-levels dictated by the radiation intensity from the illuminating laser. The work has been carried out for the Department of Mathematics at KTH Royal Institute of Technology and the Advanced Light Microscopy facility at the Science for Life Laboratory in Stockholm.