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.

中文翻译：

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荧光显微镜图像去噪的方差下限

由于预期的低光子预算，高速荧光显微镜的信噪比受到光子计数噪声和传感器噪声的严重影响。通过结合有关成像系统或生物样本的额外知识或假设，开发了去噪算法以减少显微镜数据中的这些噪声波动。出现了一个问题：显微镜去噪算法的性能是否存在理论精度限制。在本文中，将 Cramér-Rao 下界与约束条件和显微镜系统的低通滤波器特性相结合，我们开发了一种计算显微镜图像去噪的理论方差下界的方法。我们表明该下限受光子计数、读出噪声、检测波长、显微镜系统的有效像素大小和数值孔径。我们通过将多种最先进的去噪算法与此界限进行比较来展示我们的发展。该方法建立了一个框架，在特定的先验知识或假设下生成理论性能极限，作为显微镜去噪算法的参考基准。