Multiple hypothesis tracking (MHT) is a preferred technique for solving the data association problem in modern multiple target tracking systems. However in bioimaging applications, its use has long been thought impossible due to the prohibitive cost induced by the high number of objects that need to be tracked and the poor quality of images. We show in this paper that this broadly accepted view should change. We propose a MHT algorithm (fMHT) that is fast even when dealing with very noisy images of very numerous targets. We have applied the method to the analysis of two sets of real microscopy images that contain thousands of biological targets. By doing so we prove the benefits of the approach when tracking in very noisy environments such as low-light level fluorescent microscopy images.