Joint state recognition in scanning probe microscopy using spatial-frequency and scan-context learning

Accurate image state recognition is essential for autonomous scanning probe microscopy (SPM), where a single image may simultaneously reflect imaging quality, surface morphology, sample condition and probe-tip state. However, these state attributes are strongly coupled in real SPM acquisition tasks, making conventional single-task or purely spatial-domain classifiers insufficient for reliable joint multi-task recognition. To address this problem, we propose SFDR-ResMamba, a four-task multi-output SPM image classification framework for jointly predicting image quality, image type, sample state, and tip state. The proposed method first constructs a spatial-frequency dual-domain representation (SFDR), which integrates a spatial-enhanced view, a full-band Fourier amplitude view, and a scan-line-direction high-pass reconstruction view to encode local morphology, global periodicity, and scan-related frequency cues. A residual scan-context Mamba encoder is then designed to combine the local inductive bias of residual convolution with row-wise and column-wise Mamba context modeling, enabling efficient representation of raster-scan dependencies and two-dimensional structural continuity. To reduce semantic interference among the four tasks, a task-aware residual gated decoupling (TAR-GD) module further generates task-specific residual features from multi-level representations. Experiments on the MSPM-10K dataset demonstrate that SFDR-ResMamba outperforms representative CNN, efficient CNN, Transformer and Mamba-based baselines, achieving a mean accuracy of 92.6\% and a mean Macro-F1 of 90.9\%. Ablation studies, conditional performance analysis, and joint correctness evaluation support the contributions of the proposed spatial-frequency representation, scan-context modeling, and task-aware decoupling strategy, while feature visualization provides a qualitative view of the learned tip-state representations.