Bayes-optimal detectors design using relevant second-order criteria

Cédric Richard (1) , Régis Lengellé (1) , Fahed Abdallah (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

Statistical detection theories lead to the fundamental result that the optimum test consists in comparing any strictly monotone function of the likelihood ratio with a threshold value. In many applications, implementing such a test may be impossible. Therefore, we are often led to consider a simpler procedure for designing detectors. In particular, we can use alternative design criteria such as second-order measures of quality. A necessary and sufficient condition is given for such criteria to guarantee the best solution in the sense of classical detection theories. This result is illustrated by discussing the relevance of well-known criteria.

Keywords: —Bayes-optimal detector; deflection; detector design; Fisher criterion; generalized signal-to-noise ratio; second-order criterion

Domains: Signal and Image processing

Cédric Richard, Régis Lengellé, Fahed Abdallah. Bayes-optimal detectors design using relevant second-order criteria. IEEE Signal Processing Letters, 2002, 9 (1), pp.32-33. ⟨10.1109/97.988723⟩. ⟨hal-02303705⟩