Variance lower bound on fluorescence microscopy image denoising.

Yilun Li,Sheng Liu,Fang Huang

doi:10.1364/boe.401836

Abstract

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.

Highlights

Rapid development of fluorescent microscopy techniques together with the availability of fast and sensitive cameras are enabling molecular observations at unprecedented spatial and temporal resolution
The signal to noise ratio (SNR) of a microscopy image decreases rapidly with decreasing number of detected photon. At these low light conditions, quantitative biological measurements result in imprecisions — fluctuations of measured signal mainly come from the uncertainty of photon detection rather than the underlying biological processes
Our target here is to develop a variance lower bound for microscopy denoising algorithms by considering the common property of a far-field optical microscope system: the frequency response of a microscope is characterized by its optical transfer function (OTF) [8]

Summary

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. In this paper, combining Cramér-Rao Lower Bound with constraints and the low-pass-filter property of microscope systems, we develop a method providing 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.

By defining

Findings

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