Performance analysis and improvement of dither modulation under the composite attacks
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RESEARCH
Open Access
Performance analysis and improvement of dither modulation under the composite attacks Xinshan Zhu1,2* and Jie Ding1,3
Abstract The first goal of this article is to analyze the performance of dither modulation (DM) against the composite attacks including valumetric scaling, additive noise and constant change. The analyzes are developed under the assumptions that the host vector and noise vector are mutually independent and both of them have independently and identically distributed components. We derive the general expressions of the probability density functions of several concerned signals and the decoding error probability. The specific theoretical results are provided for the case of generalized Gaussian host and noise. Based on the analyzes, the performance of DM is predicted for different scenarios with a high degree of accuracy and evaluated for different distribution models of host and noise signals. Numerical simulations confirm the validity of the given theoretical analyzes. Then, we address to improve the robustness of DM against valumetric scaling plus constant change. The normalized dither modulation (NDM) is presented, which works by constructing a gain-invariant vector with zero mean for quantization. Performance analysis shows that NDM is theoretically invariant to valumetric scaling and constant change and achieves similar performance to DM in other aspects. The performance of NDM is further improved by weighting the quantization errors. Experiments on real images also show the advantage of NDM over DM subject to amplitude scaling and constant change. Keywords: digital watermarking, quantization index modulation, composite attacks, valumetric scaling, constant change
1 Introduction In the past decade, much attention has been paid to the quantization-based watermarking for canceling the host signal interference. One of the most important methods proposed so far is quantization index modulation (QIM) [1]. The basic QIM algorithm includes a number of variants, i.e., dither modulation (DM), distortion compensated dither modulation (DC-DM) (also known as scalar Costa scheme (SCS) [2]) and spread transform dither modulation (STDM) [1]. The theoretical performance of QIM methods is a key issue and has received considerable attention. Initially, the Gaussian channel is often used in the analyzes and the performance of QIM methods has been extensively investigated in this case. A relatively crude approximation to the decoding error probability * Correspondence: [email protected] 1 School of Information Engineering, Yangzhou University, Yangzhou 225009, China Full list of author information is available at the end of the article
of QIM was given in [1] for the additive white Gaussian noise (AWGN) attacks. The performance of SCS was completely analyzed by Eggers et al. [2] under the AWGN attacks. In [3], the performance of scalar DCQIM against AWGN was theoretically evaluated from the detection viewpoint. Recently, a new logarithmic QIM (LQIM) was presented in [4] and its performan
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