Real-world graph observations may contain local corruptions by abnormal behaviors. While existing research usually pursues global smoothness in graph embedding, these rarely observed anomalies are harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects corrupted node attributes and recovers robust embedding for prediction tasks. The detection operation does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. We alleviate an inertial alternating direction method of multipliers to approach a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments validate the model recovers robust graph representations from black-box poisoning and achieves excellent performance.