Self-Tuning Regularization for Image Scanning Microscopy
This work provides a more robust and stable image reconstruction method for researchers and practitioners using Image Scanning Microscopy, especially in challenging low-photon conditions, by addressing the noise amplification and artifact issues of existing deconvolution techniques.
This paper introduces a self-tuning explicit regularization framework for Multi-Image Deconvolution (MID) and super-resolution sectioning ISM (s^2ISM) reconstruction methods, which typically suffer from noise amplification and artifacts due to semi-convergent iterative schemes. The framework combines a multi-frame Poisson data fidelity term with explicit regularization (e.g., L1 and smoothed total variation penalties) and an automatic, ground-truth-free regularization parameter selection strategy. This results in improved reconstruction stability and image quality, particularly in low-photon conditions, compared to unregularized approaches.
Image Scanning Microscopy (ISM) is a fluorescence imaging technique that combines detector-array acquisition and computational reconstruction to achieve the theoretical resolution of an ideal confocal microscope, i.e., one operating with an infinitesimally small pinhole, while maintaining high signal-to-noise ratio. Among the reconstruction methods for obtaining the super-resolved image, multi-image deconvolution (MID) and its extension aimed at preserving the optical sectioning capability of confocal microscopy, known as super-resolution sectioning ISM (s$^2$ISM), are among the most widely used approaches. Both methods rely on Richardson--Lucy-type iterative schemes, whose semi-convergent behavior requires early stopping and often leads to noise amplification and reconstruction artifacts. In this work, we introduce a self-tuning explicit regularization framework for both MID and s$^2$ISM reconstruction. Within a Bayesian maximum a posteriori formulation, we combine a multi-frame Poisson data fidelity term with explicit regularization, considering $\ell_1$ and smoothed total variation penalties as representative examples. We further develop an automatic and ground-truth-free strategy for regularization parameter selection by adapting the residual whiteness principle to the multi-frame Poisson setting and introducing a spectral high-pass extension tailored to s$^2$ISM. The resulting framework enables stable reconstructions without empirical stopping rules. To demonstrate the proposed framework, we consider first-order optimization schemes based on proximal gradient and mirror descent methods with adaptive backtracking strategies. Experiments on simulated and real fluorescence ISM datasets demonstrate improved reconstruction stability and image quality with respect to unregularized approaches, while enabling robust super-resolution and optical sectioning in low-photon conditions.