Photoblinking/photobleaching differential equation model for intensity decay of fluorescence microscopy images

Fluorescence confocal microscopy images are affected by fading effects, such as photoblinking and photobleaching, that leads to image intensity decreasing along the time, preventing long exposure time experiments. These fading effects increase with the amount of radiation that illuminates the speciem. Additionally, these type of images present a low signal to noise ratio and are corrupted by a type of multiplicative noise with Poisson distribution due to the strong amplification needed to observe the small fluorescent radiation emitted by the fluorosphore. Therefore a trade-off exists between the needs of increasing the incident radiation to improve the signal to noise ratio and the needs of decreasing that radiation to minimize the fading effects. The main goal of this paper is to obtain an intensity decay law to describe the photoblinking/photobleaching effect based on a theoretical model derived from the quantic phenomena described in the literature, involved in the process. The decay law, derived here from the theoretical model, matches the intensity decay law that is usually referred in the literature, obtained from experimental data. The model is plugged in a Bayesian denoising algorithm that takes into account the temporal correlation among consecutive images to improve its visualization, mainly in the last ones where the intensity is very small. Results with real data is presented to illustrate the validity of the model.