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Automatically identifying the structural substrates underlying cardiac abnormalities can potentially provide real-time guidance for interventional procedures. With the knowledge of cardiac tissue substrates, the treatment of complex arrhythmias such as atrial fibrillation and ventricular tachycardia can be further optimized by detecting arrhythmia substrates to target for treatment (i.e., adipose) and identifying critical structures to avoid. Optical coherence tomography (OCT) is a real-time imaging modality that aids in addressing this need. Existing approaches for cardiac image analysis mainly rely on fully supervised learning techniques, which suffer from the drawback of workload on labor-intensive annotation process of pixel-wise labeling. To lessen the need for pixel-wise labeling, we develop a two-stage deep learning framework for cardiac adipose tissue segmentation using image-level annotations on OCT images of human cardiac substrates. In particular, we integrate class activation mapping with superpixel segmentation to solve the sparse tissue seed challenge raised in cardiac tissue segmentation. Our study bridges the gap between the demand on automatic tissue analysis and the lack of high-quality pixel-wise annotations. To the best of our knowledge, this is the first study that attempts to address cardiac tissue segmentation on OCT images via weakly supervised learning techniques. Within an in-vitro human cardiac OCT dataset, we demonstrate that our weakly supervised approach on image-level annotations achieves comparable performance as fully supervised methods trained on pixel-wise annotations.