Reconstruction and regularization approaches for image scanning microscopy

Confocal laser-scanning microscopy (CLSM), one of the most important imaging tools in biomedical and biological research, is undergoing a major transition towards image-scanning microscopy (ISM). In ISM, a fast detector array replaces the conventional single-element detector and pinhole of the confocal microscope, providing a true image of the region probed during laser scanning while collecting the majority of photons emitted by the specimen. By reconstructing this highly informative dataset, ISM produces images that overcome the traditional trade-off between transverse spatial resolution and signal-to-noise ratio (SNR) that limits confocal microscopy. This transition is further driven by the introduction of single-photon avalanche diode (SPAD) array detectors, whose single-photon timing capabilities and asynchronous readout enable seamless integration with fluorescence lifetime imaging microscopy (FLIM) – one of the most powerful and widely used applications of CLSM – and fluorescence signal sampling at sub-microsecond temporal resolution. However, current ISM reconstruction algorithms face several limitations. First, they lack optical sectioning and fail with thick samples unless the detector size is reduced to act as a pinhole, thereby introducing a new trade-off between sectioning capability and SNR. Second, they are not optimised for FLIM. Finally, the most advanced ISM reconstruction methods are prone to artefacts caused by noise amplification, particularly when iterative optimisation is not properly regularised. In this work, we propose a method that overcomes these limitations. Based on the observation that detector arrays inherently encode axial information from the specimen, we developed a maximum-likelihood estimation (MLE) reconstruction algorithm, termed s²ISM (super-resolved sectioned ISM), which inverts the physical model of ISM image formation. From a single-plane ISM acquisition, s²ISM reconstructs images with super-resolution, high SNR, and enhanced optical sectioning. Within the MLE framework, s²ISM also exploits the redundant information contained in the ISM dataset to achieve digital super-resolution. We further extend s²ISM to FLIM by incorporating the instrument response function (IRF) of the system into the image-formation model to compensate for temporal distortions. The resulting s²FLISM algorithm provides super-resolved FLIM images with enhanced optical sectioning and robust lifetime estimation. Moreover, we introduce a modified version of s²FLISM that enables lifetime-based multi-target imaging, allowing distinct fluorophores to be separated based on their fluorescence lifetimes rather than their spectral properties. Finally, we address the noise amplification inherent to maximum-likelihood estimation by leveraging the SPAD array’s temporal sampling capabilities to implement an integrated denoising framework. This strategy effectively suppresses noise amplification, enhances numerical stability, and improves the robustness of the reconstruction process. We validate our method through a comprehensive theoretical analysis and experimental results obtained from calibration standards and biological specimens imaged with a custom-built linear and non-linear laser-scanning microscope equipped with a SPAD array detector. We believe that s²ISM and its lifetime-resolved extension s²FLISM represent a significant advancement for ISM, establishing a unified and versatile framework for super-resolved, lifetime-resolved, and optically sectioned fluorescence microscopy. This approach paves the way for new imaging modalities capable of addressing increasingly complex questions in biological and biomedical research.