  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.
