Self-Tuning Regularization for Image Scanning Microscopy

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.

Reconstructing the Image Scanning Microscopy Dataset: an Inverse Problem

Confocal laser-scanning microscopy (CLSM) is one of the most popular optical architectures for fluorescence imaging. In CLSM, a focused laser beam excites the fluorescence emission from a specific specimen position. Some actuators scan the probed region across the sample and a photodetector collects a single intensity value for each scan point, building a two-dimensional image pixel-by-pixel. Recently, new fast single-photon array detectors have allowed the recording of a full bi-dimensional image of the probed region for each scan point, transforming CLSM into image scanning microscopy (ISM). This latter offers significant improvements over traditional imaging but requires an optimal processing tool to extract a super-resolved image from the four-dimensional dataset. Here we describe the image formation process in ISM from a statistical point of view, and we use the Bayesian framework to formulate a multi-image deconvolution problem. Notably, the single-photon detector suffers exclusively from the photon shot noise, enabling the development of an effective likelihood model. We derive an iterative likelihood maximization algorithm and test it on experimental and simulated data. Furthermore, we demonstrate that the ISM dataset is redundant, enabling the possibility of obtaining reconstruction sampled at twice the scanning step. Our results prove that in ISM, under appropriate conditions, the Nyquist-Shannon sampling criterium is effectively relaxed. This finding can be exploited to speed up the acquisition process by a factor of four, further improving the versatility of ISM systems.