# Self-Tuning Regularization for Image Scanning Microscopy

arXiv: https://arxiv.org/abs/2605.31426 · HTML: https://mlsanity.com/paper/2605.31426/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 12 of 12)

- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems](https://mlsanity.com/paper/2306.03466/) (2023)
- [MicroSSIM: Improved Structural Similarity for Comparing Microscopy Data](https://mlsanity.com/paper/2408.08747/) (2024)
- [Backtracking strategies for accelerated descent methods with smooth composite objectives](https://mlsanity.com/paper/1709.09004/) (2017)
- [Deep Equilibrium models for Poisson Imaging Inverse problems via Mirror Descent](https://mlsanity.com/paper/2507.11461/) (2025)
- [Scaled, inexact and adaptive generalized FISTA for strongly convex optimization](https://mlsanity.com/paper/2101.03915/) (2021)
- [Reconstructing the Image Scanning Microscopy Dataset: an Inverse Problem](https://mlsanity.com/paper/2211.12510/) (2022)
- [Whiteness-based bilevel learning of regularization parameters in imaging](https://mlsanity.com/paper/2403.07026/) (2024)
- [Whiteness-based bilevel estimation of weighted TV parameter maps for image denoising](https://mlsanity.com/paper/2503.07814/) (2025)

## Abstract (arXiv)

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.