In this paper, a multi-scale approach to spectrum sensing in cognitive cellular networks is proposed. In order to overcome the huge cost incurred in the acquisition of full network state information, a hierarchical scheme is proposed, based on which local state estimates are aggregated up the hierarchy to obtain aggregate state information at multiple scales, which are then sent back to each cell for local decision making. Thus, each cell obtains fine-grained estimates of the channel occupancies of nearby cells, but coarse-grained estimates of those of distant cells. The performance of the aggregation scheme is studied in terms of the trade-off between the throughput achievable by secondary users and the interference generated by the activity of these secondary users to primary users. In order to account for the irregular structure of interference patterns arising from path loss, shadowing, and blockages, which are especially relevant in millimeter wave networks, a greedy algorithm is proposed to find a multi-scale aggregation tree to optimize the performance. It is shown numerically that this tailored hierarchy outperforms a regular tree construction by 60%.