Background: Electrocardiograms are indispensable for diagnosing cardiovascular diseases, yet in many settings they exist only as paper printouts stored in multiple recording layouts. Converting these images into digital signals introduces two key challenges: temporal asynchrony among leads and partial blackout missing, where contiguous signal segments become entirely unavailable. Existing models cannot adequately handle these concurrent problems while maintaining interpretability. Methods: We propose PatchECG, combining an adaptive variable block count missing learning mechanism with a masked training strategy. The model segments each lead into fixed-length patches, discards entirely missing patches, and encodes the remainder via a pluggable patch encoder. A disordered patch attention mechanism with patch-level temporal and lead embeddings captures cross-lead and temporal dependencies without interpolation. PatchECG was trained on PTB-XL and evaluated under seven simulated layout conditions, with external validation on 400 real ECG images from Chaoyang Hospital across three clinical layouts. Results: PatchECG achieves an average AUROC of approximately 0.835 across all simulated layouts. On the Chaoyang cohort, the model attains an overall AUROC of 0.778 for atrial fibrillation detection, rising to 0.893 on the 12x1 subset -- surpassing the pre-trained baseline by 0.111 and 0.190, respectively. Model attention aligns with cardiologist annotations at a rate approaching inter-clinician agreement. Conclusions: PatchECG provides a robust, interpolation-free, and interpretable solution for arrhythmia detection from digitized ECG images across diverse layouts. Its direct modeling of asynchronous and partially missing signals, combined with clinically aligned attention, positions it as a practical tool for cardiac diagnostics from legacy ECG archives in real-world clinical environments.

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