Re-thinking Richardson-Lucy without Iteration Cutoffs: Physically Motivated Bayesian Deconvolution

TL;DR

This paper introduces a Bayesian deconvolution method that models image formation accurately, avoids iterative cutoff tuning, and produces stable, positive solutions without overfitting noise, improving upon traditional Richardson-Lucy techniques.

Contribution

The authors develop a physically motivated Bayesian deconvolution framework that eliminates the need for iteration cutoffs and regularizers, providing stable, unsupervised, and positive solutions.

Findings

Achieves deconvolution in the spatial domain with full noise modeling

Provides stable, parameter-free inference converging without user tuning

Enables fast, parallelizable computation for practical use

Abstract

Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is achieved by iteratively maximizing a Poisson emission likelihood. However, the RL algorithm is known to prefer sparse solutions and overfit noise, leading to high-frequency artifacts. The structure of these artifacts is sensitive to the number of RL iterations, and this parameter is typically hand-tuned to achieve reasonable perceptual quality of the inferred object. Overfitting can be mitigated by introducing tunable regularizers or other ad hoc iteration cutoffs in the optimization as otherwise incorporating fully realistic models can introduce computational bottlenecks. To resolve these problems, we present Bayesian deconvolution, a rigorous deconvolution framework that combines a physically accurate image formation model avoiding the challenges inherent to the RL approach. Our approach achieves deconvolution while satisfying the following desiderata: I deconvolution is performed in the spatial domain (as opposed to the frequency domain) where all known noise sources are accurately modeled and integrated in the spirit of providing full probability distributions over the density of the putative object recovered; II the probability distribution is estimated without making assumptions on the sparsity or continuity of the underlying object; III unsupervised inference is performed and converges to a stable solution with no user-dependent parameter tuning or iteration cutoff; IV deconvolution produces strictly positive solutions; and V implementation is amenable to fast, parallelizable computation.