Complex-valued Retrievals From Noisy Images Using Diffusion Models

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.Comment: 11 pages, 7figure

Multi-View Polarimetric Scattering Cloud Tomography and Retrieval of Droplet Size

Tomography aims to recover a three-dimensional (3D) density map of a medium or an object. In medical imaging, it is extensively used for diagnostics via X-ray computed tomography (CT). We define and derive a tomography of cloud droplet distributions via passive remote sensing. We use multi-view polarimetric images to fit a 3D polarized radiative transfer (RT) forward model. Our motivation is 3D volumetric probing of vertically-developed convectively-driven clouds that are ill-served by current methods in operational passive remote sensing. Current techniques are based on strictly 1D RT modeling and applied to a single cloudy pixel, where cloud geometry defaults to that of a plane-parallel slab. Incident unpolarized sunlight, once scattered by cloud-droplets, changes its polarization state according to droplet size. Therefore, polarimetric measurements in the rainbow and glory angular regions can be used to infer the droplet size distribution. This work defines and derives a framework for a full 3D tomography of cloud droplets for both their mass concentration in space and their distribution across a range of sizes. This 3D retrieval of key microphysical properties is made tractable by our novel approach that involves a restructuring and differentiation of an open-source polarized 3D RT code to accommodate a special two-step optimization technique. Physically-realistic synthetic clouds are used to demonstrate the methodology with rigorous uncertainty quantification