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Segmentation of 3D knee MR images is important for the assessment of osteoarthritis. Like other medical data, the volume-wise labeling of knee MR images is expertise-demanded and time-consuming; hence semi-supervised learning (SSL), particularly barely-supervised learning, is highly desirable for training with insufficient labeled data. We observed that the class imbalance problem is severe in the knee MR images as the cartilages only occupy 6% of foreground volumes, and the situation becomes worse without sufficient labeled data. To address the above problem, we present a novel framework for barely-supervised knee segmentation with noisy and imbalanced labels. Our framework leverages label distribution to encourage the network to put more effort into learning cartilage parts. Specifically, we utilize 1.) label quantity distribution for modifying the objective loss function to a class-aware weighted form and 2.) label position distribution for constructing a cropping probability mask to crop more sub-volumes in cartilage areas from both labeled and unlabeled inputs. In addition, we design dual uncertainty-aware sampling supervision to enhance the supervision of low-confident categories for efficient unsupervised learning. Experiments show that our proposed framework brings significant improvements by incorporating the unlabeled data and alleviating the problem of class imbalance. More importantly, our method outperforms the state-of-the-art SSL methods, demonstrating the potential of our framework for the more challenging SSL setting.