Asymptotically Optimal Scalar Quantizers for QIM Watermark Detection

This paper investigates asymptotically optimal scalar quantizers to address QIM watermark detection with i.i.d. host data and additive noise. False-alarm probability of detection is chosen as the cost to be minimized, keeping the embedding distortion and the miss probability upper-bounded. To avoid the intractability of false-alarm probability, Kullback distance between watermarked and non-watermarked data is adopted instead. The problem is then to seek the quantizer which maximizes the false-alarm error exponent under distortion constraint. Using Lagrange multiplier minimization, a quantizer updating Lloyd-Max-like procedure is used to solve the optimization. For experimental aspects, host data and noise have been set Gaussian. In comparison with uniform or Lloyd-Max quantizers, it turns out that detection performances can be notably enhanced by using proposed application-optimized quantizers. The gain is effective even for small number TV of sample at the detector input. However, this gain becomes more substantial as TV grows. This also emphasises that good quantizers in terms of distortion are not suitable for detection task