Fluorescent protein microscopy imaging is nowadays one of the most important tools in biomedical research. However, the resulting images present a low signal to noise ratio and a time intensity decay due to the photobleaching effect. This phenomenon is a consequence of the decreasing on the radiation emission efficiency of the tagging protein. This occurs because the fluorophore permanently loses its ability to fluoresce, due to photochemical reactions induced by the incident light. The Poisson multiplicative noise that corrupts these images, in addition with its quality degradation due to photobleaching, make long time biological observation processes very difficult. In this paper a denoising algorithm for Poisson data, where the photobleaching effect is explicitly taken into account, is described. The algorithm is designed in a Bayesian framework where the data fidelity term models the Poisson noise generation process as well as the exponential intensity decay caused by the photoble...