Self-Tuning Regularization for Image Scanning Microscopy
Authors: Sofia Agostoni, Lisa Cuneo, Christian Daniele, Giacomo Garré, Laurent Le, Alessandro Zunino, Giuseppe Vicidomini, Luca Calatroni
Abstract
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 (s2ISM), 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 s2ISM reconstruction. Within a Bayesian maximum a posteriori formulation, we combine a multi-frame Poisson data fidelity term with explicit regularization, considering ℓ1 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 s2ISM. 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.
Fluorescence microscopy images are degraded by noise and diffraction-induced blur, which compromise structural fidelity and limit quantitative analysis. Supervised deep learning methods achieve impressive restoration performance but require large-scale paired datasets that are difficult to obtain in practice. To address this issue, we propose SDIP, a zero-shot deep image prior (DIP) framework that sequentially performs denoising and deconvolution without external training data. An aSeqDIP-based module first suppresses noise while preserving fine structures through sequential autoencoding regularization. In the deconvolution stage, a wavelet-based background correction step is incorporated before the proposed RLG-DIP module performs artifact-reduced deconvolution. RLG-DIP uses the Richardson-Lucy deconvolution result as a physically consistent guidance prior, integrating the imaging model with the implicit prior of DIP to stabilize the ill-posed deconvolution process. Experiments on the BioSR dataset across multiple cellular structures demonstrate that SDIP improves both signal-to-noise ratio and resolution, achieving superior visual quality and improved quantitative performance on most evaluated structures. The proposed framework may also provide useful insights for designing physically guided DIP methods for other inverse problems.
We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in scale can be achieved using sensors with different pixel sizes (as demonstrated here) or by varying the effective pixel size through changes in optical magnification (e.g., using a zoom lens). We show that images acquired with pairwise coprime pixel sizes lead to a system with a stable inverse, and furthermore, that super-resolution images can be reconstructed efficiently using Fourier domain techniques or iterative least squares methods. Our mathematical analysis provides an expression for the expected error of the least squares reconstruction for large signals assuming i.i.d. noise that elucidates the noise-resolution tradeoff. These results are validated through both one- and two-dimensional experiments that leverage charge-coupled device (CCD) hardware binning to explore reconstructions over a large range of effective pixel sizes. Finally, two-dimensional reconstructions for a series of targets are used to demonstrate the advantages of multiscale super-resolution, and implications of these results for common imaging systems are discussed.
Laser line-scanning microscopy enables fast volumetric imaging but produces anisotropic lateral resolution. Orthogonal line scans provide complementary directional information that can recover near-isotropic resolution, yet existing deep-learning methods require a separate model for each optical configuration. We present a unified, resolution-conditioned fusion framework based on Rank Enhanced Linear Attention (RELA). Feature-wise Linear Modulation (FiLM) conditions the network continuously on the resolving-power ratio, enabling one model to adapt across slit widths. We further introduce Adaptive RELA, which replaces fixed-kernel rank enhancement with ratio-conditioned multi-scale depthwise convolutions and uses a learnable attention temperature to adjust selectivity with degradation severity. Training data spanning multiple slit configurations are generated using a physics-grounded separable point-spread-function model verified against measured optical data at 48.3 dB accuracy. The resulting model achieves 34-40 dB PSNR across configurations, whereas unconditioned multi-slit training collapses to 24.3 dB and per-slit specialists lose 4-9 dB outside their training setting. It also generalizes smoothly to unseen intermediate configurations without interpolation artifacts. Ablations show that FiLM resolves configuration ambiguity, global linear attention captures long-range directional correspondences, and adaptive temperature yields an additional 2 dB in the challenging near-isotropic regime, where complementary signals are weak.