AI 中文总结
本研究将扫描探针显微镜图像重建视为贝叶斯顺序状态估计问题，结合前向卡尔曼滤波与RTS后向滤波，实现高效重建并输出不确定性图与诊断信号。
AI 中文摘要
扫描探针显微镜（SPM）已成为材料科学、凝聚态物理、纳米技术、生物学和半导体计量学的主流工具。然而，SPM图像是在探针在闭环反馈下穿越表面时顺序采集的，而热漂移、反馈动力学、针尖状态、机械扰动和电子噪声在实验过程中不断演变。因此，图像校正已成为SPM数据分析中不可或缺的一部分。经典方法依赖于线调平、滤波、配准、插值以及针尖或扫描器畸变的显式模型，而近期工作越来越多地使用经训练将损坏图像映射为校正图像的神经网络。在此，我们探索一种不同的表述，将SPM重建视为贝叶斯顺序状态估计问题。隐藏状态表示表面高度及其沿慢扫描方向的低阶演化；一个与伪影相关的质量分数持续修改观测似然；前向卡尔曼滤波通过提供因果估计和创新诊断；而Rauch-Tung-Striebel（RTS）后向滤波通过纳入完整采集的信息。结果是重建表面、相对后验不确定性图以及线分辨诊断信号。该递归计算轻量，且随图像像素数线性扩展，而物理参数原则上可从仪器表征或先前操作中学习的先验初始化，此扩展未在此处实施。我们将该方法组织为多轴模型族，以便独立评估状态表示、伪影识别、横向耦合和采集冗余的贡献。
英文摘要
Scanning probe microscopy (SPM) has become a mainstay of materials science, condensed matter physics, nanotechnology, biology, and semiconductor metrology. An SPM image, however, is acquired sequentially as the probe traverses the surface under closed-loop feedback while thermal drift, feedback dynamics, tip state, mechanical disturbances, and electronic noise evolve during the experiment. Image correction has therefore become an intrinsic part of SPM data analysis. Classical approaches rely on line leveling, filtering, registration, interpolation, and explicit models of tip or scanner distortions, whereas recent work increasingly uses neural networks trained to map corrupted images to corrected ones. Here, we explore a different formulation in which SPM reconstruction is treated as a Bayesian sequential state-estimation problem. The hidden state represents surface height and its low-order evolution along the slow-scan direction; an artifact-dependent quality score continuously modifies the observation likelihood; a forward Kalman pass provides the causal estimate and innovation diagnostics; and a Rauch-Tung-Striebel (RTS) backward pass incorporates information from the complete acquisition. The result is a reconstructed surface, a relative posterior uncertainty map, and line-resolved diagnostic signals. The recursion is computationally lightweight and scales linearly with the number of image pixels, while the physical parameters can in principle be initialized from instrument characterization or from priors learned during previous operation, an extension not exercised here. We organize the method as a multi-axis family of models so that the contributions of state representation, artifact recognition, lateral coupling, and acquisition redundancy can be evaluated independently.
