In diverse microscopy modalities, sensors measure only real-valued intensities. Additionally, the sensor readouts are affected by Poissonian-distributed photon noise. Traditional restoration algorithms typically aim to minimize the mean squared error (MSE) between the original and recovered images. This often leads to blurry outcomes with poor perceptual quality. Recently, deep diffusion models (DDMs) have proven to be highly capable of sampling images from the a-posteriori probability of the sought variables, resulting in visually pleasing high-quality images. These models have mostly been suggested for real-valued images suffering from Gaussian noise. In this study, we generalize annealed Langevin Dynamics, a type of DDM, to tackle the fundamental challenges in optical imaging of complex-valued objects (and real images) affected by Poisson noise. We apply our algorithm to various optical scenarios, such as Fourier Ptychography, Phase Retrieval, and Poisson denoising. Our algorithm is evaluated on simulations and biological empirical data.

翻译：在多种显微成像模式中，传感器仅测量实值强度，且传感器读数受泊松分布光子噪声影响。传统复原算法通常以最小化原始图像与恢复图像之间的均方误差（MSE）为目标，这往往导致模糊结果，感知质量较差。近年来，深度扩散模型（DDMs）已被证明能从待求变量的后验概率中高效采样图像，从而生成视觉上悦目的高质量图像。这些模型主要针对受高斯噪声污染的实值图像提出。本研究将退火朗之万动力学（一种DDM）进行推广，以应对光学成像中复数域对象（及实图像）受泊松噪声影响这一根本性挑战。我们将算法应用于多种光学场景，如傅里叶叠层成像、相位恢复和泊松去噪。算法在仿真数据和生物学实测数据上进行了评估。