The increasing demand for transparent and reliable models, particularly in high-stakes decision-making areas such as medical image analysis, has led to the emergence of eXplainable Artificial Intelligence (XAI). Post-hoc XAI techniques, which aim to explain black-box models after training, have been controversial in recent works concerning their fidelity to the models' predictions. In contrast, Self-eXplainable AI (S-XAI) offers a compelling alternative by incorporating explainability directly into the training process of deep learning models. This approach allows models to generate inherent explanations that are closely aligned with their internal decision-making processes. Such enhanced transparency significantly supports the trustworthiness, robustness, and accountability of AI systems in real-world medical applications. To facilitate the development of S-XAI methods for medical image analysis, this survey presents an comprehensive review across various image modalities and clinical applications. It covers more than 200 papers from three key perspectives: 1) input explainability through the integration of explainable feature engineering and knowledge graph, 2) model explainability via attention-based learning, concept-based learning, and prototype-based learning, and 3) output explainability by providing counterfactual explanation and textual explanation. Additionally, this paper outlines the desired characteristics of explainability and existing evaluation methods for assessing explanation quality. Finally, it discusses the major challenges and future research directions in developing S-XAI for medical image analysis.

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