Analysis of Optimal Search Interval for Estimation of Modified Quantization Step Size in Quantization-Based Audio Watermark Detection

Abstract

The quantization-based watermarking schemes such as QIM or SCS are known to be very vulnerable to the amplitude modification attack. The amplitude modification attack results in the change of quantization step size so the estimation of a modified quantization step size is required before watermark detection. In this paper, we analyze the quantization error function of the audio signal having any shape of probability density function, and analytically determine the search interval that minimizes the quantization error considering both detection performance and computational complexity. It is shown that the appropriate search interval can be determined from the frame-based mean and variance of the input signal without regard to its shape of probability density function. Experimental results for real audio data verify that the derived search interval provides the accurate estimation of the modified quantization step size under amplitude modification attack.