On the Fundamental Limits of Recovering Tree Sparse Vectors from Noisy Linear Measurements

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Executive Summary

In this paper the authors establish fundamental performance limits for the task of support recovery of tree-sparse signals from noisy measurements, in settings where measurements may be obtained either non-adaptively (using a randomized Gaussian measurement strategy motivated by initial CS investigations) or by any adaptive sensing strategy. Their main results here imply that the adaptive tree sensing procedure analyzed in their previous work is nearly optimal, in the sense that no other sensing and estimation strategy can perform fundamentally better for identifying the support of tree-sparse signals.

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