Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model

Light microscopy is a widespread and inexpensive imaging technique facilitating biomedical discovery and diagnostics. However, light diffraction barrier and imperfections in optics limit the level of detail of the acquired images. The details lost can be reconstructed among others by deep learning models. Yet, deep learning models are prone to introduce artefacts and hallucinations into the reconstruction. Recent state-of-the-art image synthesis models like the denoising diffusion probabilistic models (DDPMs) are no exception to this. We propose to address this by incorporating the physical problem of microscopy image formation into the model's loss function. To overcome the lack of microscopy data, we train this model with synthetic data. We simulate the effects of the microscope optics through the theoretical point spread function and varying the noise levels to obtain synthetic data. Furthermore, we incorporate the physical model of a light microscope into the reverse process of a conditioned DDPM proposing a physics-informed DDPM (PI-DDPM). We show consistent improvement and artefact reductions when compared to model-based methods, deep-learning regression methods and regular conditioned DDPMs.