Variance lower bound on fluorescence microscopy image denoising

The signal to noise ratio of high-speed fluorescence microscopy is heavily influenced by photon counting noise and sensor noise due to the expected low photon budget. Denoising algorithms are developed to decrease these noise fluctuations in microscopy data by incorporating additional knowledge or assumptions about imaging systems or biological specimens. One question arises: whether there exists a theoretical precision limit for the performance of a microscopy denoising algorithm. In this paper, combining Cramér-Rao Lower Bound with constraints and the low-pass-filter property of microscope systems, we develop a method to calculate a theoretical variance lower bound of microscopy image denoising. We show that this lower bound is influenced by photon count, readout noise, detection wavelength, effective pixel size and the numerical aperture of the microscope system. We demonstrate our development by comparing multiple state-of-the-art denoising algorithms to this bound. This method establishes a framework to generate theoretical performance limit, under a specific prior knowledge, or assumption, as a reference benchmark for microscopy denoising algorithms.