Cognitive radio networks (CRNs) benefit from several features, such as decision-making, spectrum-awareness and reconfigurability, which enable them to perform channel recovery after operating channel failures due to the appearance of primary users or if the channel quality becomes unacceptable. As a result of their frequency and bandwidth agility, the cognitive radios can use heterogeneous channels with different parameters, such as availability, recovery time, and transmission rate. We thus propose a general hierarchical recovery model where the channels are classified based on their parameters into distinct sets. Instead of performing a flat channel search over all channels, the CRN first selects a channel set and then performs a restoration over the selected set. The decision process to select, as a function of the CRN current state and its knowledge about the different channel parameters, the best channel set to perform the restoration mechanism is the focus of this research work. We first target a two-set case and propose different heuristic algorithms to solve this selection problem. Numerical and simulation results are provided illustrating the benefits of the different decision algorithms for channel recovery over heterogeneous channels.