Complex-valued Retrievals From Noisy Images Using Diffusion Models

TL;DR

This paper extends diffusion models to reconstruct complex-valued images from noisy, real-valued measurements in microscopy, improving image quality in optical imaging tasks affected by Poisson noise.

Contribution

It introduces a generalized annealed Langevin Dynamics approach for complex-valued image retrieval under Poisson noise, applicable to various optical imaging modalities.

Findings

Effective in Fourier Ptychography, Phase Retrieval, and Poisson denoising

Produces high-quality, perceptually pleasing images

Validated on simulations and biological data

Abstract

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.