Improving Richardson--Lucy Deconvolution with Diffusion Priors for Fluorescence Microscopy

Richardson--Lucy (RL) deconvolution improves fluorescence microscopy images by recovering details lost to diffraction. It estimates the fluorescence signal most likely to have produced the measured photon counts under a Poisson imaging model. However, deconvolution remains ill-posed, especially at low photon counts, when weak biological structures become difficult to distinguish from shot noise and the prior strongly influences the reconstruction. RL recovers structure in early iterations but can amplify noise and become unstable, while regularizers such as total variation (TV) reduce these artifacts at the cost of oversmoothing. Instead, we learn a prior from real fluorescence microscopy images and use its gradient within an inverse-problem framework. The prior is estimated using an unconditional score-based diffusion model trained on a large microscopy dataset. At each step, the learned prior guides RL toward plausible specimen structures, while RL enforces Poisson consistency with the measured counts. Across diverse biological samples and cellular morphologies, the framework reduces RL noise amplification while better preserving weak structures at low photon counts.