On optimal detection for matrix multiplicative data hiding

Abstract

This paper analyzes a multiplicative data hiding scheme, where the watermark bits are embedded within frames of a Gaussian host signal by two different, but arbitrary, embedding matrices. A closed form expression for the bit error rate (BER) of the optimal detector is derived when the frame sizes tend to infinity. Furthermore, a structure is proposed for the optimal detector which divides the detection process into two main blocks: host signal estimation and decision making. The proposed structure preserves optimality, and allows for a great deal of flexibility: The estimator can be selected according to the a priori knowledge about host signal. For example, if the host signal is an Auto-Regressive (AR) process, we argue that a Kalman filter may serve as the estimator. Compared to a direct implementation of the Neyman-Pearson detector, this approach results in significantly reduced complexity while keeping optimal performance.