Anomalous signal detection and estimation on the stochastic noise background

Shakir K. Formanov; Anatoliy N. Startsev; Olimshan Sh. Sharipov; Jakhongir B. Azimov

doi:10.1117/12.692967

30 May 2006 Anomalous signal detection and estimation on the stochastic noise background

Shakir K. Formanov, Anatoliy N. Startsev, Olimshan Sh. Sharipov, Jakhongir B. Azimov

Proceedings Volume 6277, Optical Technologies for Telecommunications 2005; 62770B (2006) https://doi.org/10.1117/12.692967
Event: Optical Technologies for Telecommunications 2005, 2005, Ufa, Russian Federation

Abstract

The problem of the minimax recovery of a nonparametric two-dimensional signal blurred by some khown function and observed with additive noise is considered. The unknown function of two variables is assumed to belong to a hyperrectangle of L₂([0,1]²) Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose linear minimax estimator and show that its maximal risk attains asymptotically the minimax risk. In the case of non-Gaussian noise we propose other estimator that however is not asymptotically optimal.

Citation Download Citation

Shakir K. Formanov, Anatoliy N. Startsev, Olimshan Sh. Sharipov, and Jakhongir B. Azimov "Anomalous signal detection and estimation on the stochastic noise background", Proc. SPIE 6277, Optical Technologies for Telecommunications 2005, 62770B (30 May 2006); https://doi.org/10.1117/12.692967

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