图像扫描显微镜的自调谐正则化
Self-Tuning Regularization for Image Scanning Microscopy
AI总结：
针对图像扫描显微镜（ISM）的多图像反卷积（MID）和超分辨率切片ISM（s²ISM）重建，提出一种自调谐显式正则化框架，通过贝叶斯最大后验公式结合多帧泊松数据保真项与ℓ1或平滑全变分惩罚，并基于残差白化原则自适应选择正则化参数，无需经验停止准则，在低光子条件下实现稳定超分辨和光学切片。
摘要：
图像扫描显微镜（ISM）是一种荧光成像技术，它结合探测器阵列采集和计算重建，实现理想共聚焦显微镜（即使用无穷小针孔）的理论分辨率，同时保持高信噪比。在获得超分辨图像的重建方法中，多图像反卷积（MID）及其旨在保持共聚焦显微镜光学切片能力的扩展（称为超分辨率切片ISM，s²ISM）是最广泛使用的方法之一。这两种方法都依赖于Richardson-Lucy型迭代方案，其半收敛行为需要提前停止，并且常常导致噪声放大和重建伪影。在这项工作中，我们为MID和s²ISM重建引入了一个自调谐显式正则化框架。在贝叶斯最大后验公式中，我们将多帧泊松数据保真项与显式正则化相结合，考虑ℓ1和平滑全变差惩罚作为代表性例子。我们进一步通过将残差白化原则适应于多帧泊松设置，并引入针对s²ISM定制的频谱高通扩展，开发了一种自动且无需真实值的正则化参数选择策略。由此产生的框架无需经验停止规则即可实现稳定重建。为了演示所提出的框架，我们考虑了基于近端梯度和镜像下降方法的一阶优化方案，并采用自适应回溯策略。在模拟和真实荧光ISM数据集上的实验表明，与无正则化方法相比，重建稳定性和图像质量得到改善，同时在低光子条件下实现了鲁棒的超分辨率和光学切片。
英文摘要：
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.
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