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Limits to estimation in stochastic ill-conditioned inverse problems

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1 Author(s)
Solo, V. ; Dept. of Stat., Macquarie Univ., Sydney, NSW, Australia

Using information-theoretic methods we develop simple results quantifying a lower bound for minimax estimation, a kind of infinite-dimensional Cramer-Rao lower bound, for signal estimation in possibly nonlinear, ill-conditioned, inverse problems. Our results reduce calculation to a geometric computation based on a modulus of continuity and make explicit connections with results in the literature on deterministic ill-conditioned inverse problems. Several applications are discussed

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 5 )