Independent noise realizations enable morphologically agnostic image reconstruction in single-photon-sensitive microscopy

Abstract

Advances in single-photon sensitive detectors are rapidly expanding the adoption of photon-counting fluorescence microscopy. Under the Poisson photon-counting statistics, iterative Richardson-Lucy (RL) -type algorithms are statistically optimal for image deconvolution but suffers from a fundamental semi-convergent behaviour: prolonged iterations inevitably amplify noise, requiring heuristic early stopping or regularisation typically based on assumptions about object morphology. Here we present a morphology-agnostic regularisation framework for RL deconvolution that exploits independent noise realisations instead of structural object priors. Preserving the Poisson statistics of the acquisition process, we formulate the Regularized by Noise (RbN): a regularized variational framework and its corresponding iterative minimization algorithm that exploit the statistical consistency of independent noise realisations to distinguish reproducible image features from stochastic noise. The regularisation strength is selected automatically using the Poisson residual whiteness principle, resulting in a fully data-driven reconstruction without heuristic parameter tuning. Photon-timing-resolved systems naturally provide the independent noise realisations exploited by our framework, whereas computational photon splitting provides a statistically equivalent implementation for photon-counting systems. We validate the approach experimentally using photon-timing-resolved confocal microscopy and image scanning microscopy across eight morphologically distinct subcellular targets, and further demonstrate its applicability to photon-counting microscopes through computational photon splitting. Across imaging modalities, detector technologies, biological structures and signal-to-noise regimes, our method eliminates RL semi-convergence, removes sensitivity to the stopping criterion, and consistently outperforms conventional RL while preserving fine structural detail. More broadly, our results establish independent noise realisations as a general source of morphology-agnostic regularisation. Although demonstrated here for SPAD-based laser-scanning microscopy and Poisson statistics, the underlying principle could be extended to other imaging modalities and, more generally, to statistical inverse problems through appropriate noise-specific formulations.