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We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multiscale search algorithm that significantly reduces the search time of the adaptive resource allocation policy (ARAP) introduced in [Bashan 2008]. Similarly to ARAP, the proposed approach scans a Q-cell partition of the search area in two stages: first the entire domain is scanned and second a subset of the domain, suspected of containing targets, is rescanned. The search strategy of the proposed algorithm is driven by maximization of a modified version of the previously introduced ARAP objective function, which is a surrogate for energy constrained target detection performance. We analyze the performance of the proposed multistage ARAP approach and show that it can reduce mean search time with respect to ARAP for equivalent energy constrained detection performance. To illustrate the potential gains of M-ARAP, we simulate a moving target indicator (MTI) radar system and show that M-ARAP achieves an estimation performance gain of 7 dB and a 85% reduction in scan time as compared to an exhaustive search. This comes within 1 dB of the previously introduced ARAP algorithm at a fraction of its required scan time.