Abstract:Deep learning has achieved significant breakthroughs in medical imaging, but these advancements are often dependent on large, well-annotated datasets. However, obtaining such datasets poses a significant challenge, as it requires time-consuming and labor-intensive annotations from medical experts. Consequently, there is growing interest in learning paradigms such as incomplete, inexact, and absent supervision, which are designed to operate under limited, inexact, or missing labels. This survey categorizes and reviews the evolving research in these areas, analyzing around 600 notable contributions since 2018. It covers tasks such as image classification, segmentation, and detection across various medical application areas, including but not limited to brain, chest, and cardiac imaging. We attempt to establish the relationships among existing research studies in related areas. We provide formal definitions of different learning paradigms and offer a comprehensive summary and interpretation of various learning mechanisms and strategies, aiding readers in better understanding the current research landscape and ideas. We also discuss potential future research challenges.