Cognitive radios (CR) are an efficient approach to deploy a secondary network in the vacant portions of the spectrum licensed to primary networks. However, when primary users return to a channel used by a CR, the later should vacate the channel and start a restoration process by searching and sensing other channels. The restoration process objective is to find the best channel in the shortest time. We propose in this paper a framework where the intrinsic features of learning and history-awareness of CRs are used to improve the restoration mechanism performance by providing a shorter restoration time or a restored channel with a higher quality. We study both distributed and centralized history-aware restoration schemes and show that it can provide significant improvements for both schemes. However, history-awareness should be carefully used in distributed algorithms since it can be detrimental in certain cases due to the increased users' contention for the best channels.