Journal Article

Image Watermarking Based on Exponentiated Cauchy–Rayleigh Distribution

Niu, Pan-pan, Ma, Run-tong, Wang, Hong-xin

2025

Overview

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we propose a statistical image watermark decoder in undecimated discrete wavelet transform-polar complex exponentiated transform magnitude domain, wherein a probability density function based on the exponentiated Cauchy–Rayleigh distribution is used, in view of the fact that this probability density function provides a better statistical match to the empirical probability density function of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. In watermark embedding, we first perform the undecimated discrete wavelet transform on the carrier image. We then select the maximum energy subband and divide it into blocks, and compute the polar complex exponentiated transform for each block. Finally, we embed watermark in undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes using nonlinear multiplicative approach. In the decoding process, we first analyze the robustness and statistical characteristics of undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes. We then observe that, with a small number of parameters, the new exponentiated Cauchy–Rayleigh model can capture accurately the statistical distributions of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. Meanwhile, statistical model parameters can be estimated effectively by using genetic simulated annealing based maximum likelihood approach. Motivated by our modeling results, we finally design a new statistical image watermark decoder using the exponentiated Cauchy–Rayleigh distribution and maximum likelihood decision rule. Experimental results on extensive test images demonstrate that the proposed watermark decoder provides a performance better than that of most of the state-of-the-art methods recently proposed in the literature.

• Publisher: Springer US,Springer Nature B.V
• Subject: Circuits and Systems / Decoding / Discrete Wavelet Transform / Electrical Engineering / Electronics and Microelectronics / Engineering / Instrumentation / Maximum likelihood decoding / Maximum likelihood estimates / Parameter estimation / Parameter robustness / Probability density functions / Rayleigh distribution / Robustness / Signal,Image and Speech Processing / Simulated annealing / Statistical analysis / Statistical distributions / Statistical models / Watermarking / Wavelet analysis / Wavelet transforms