Summary: This paper addresses the problem of image recovery from partially given data in both the image and tight frame transform domains. Motivated by an uncertainty principle, a sufficient condition that ensures the exact recovery of an image is derived. Then an analysis-based model is proposed to handle situations in which exact recovery is impossible, such as when insufficient or only inaccurate data are available. An efficient iterative algorithm is obtained for the model by applying the split Bregman method. Several numerical examples are presented to demonstrate the potential of the algorithm.