Condition for Energy Efficient Watermarking with Random Vector Model without WSS Assumption

TL;DR

This paper derives conditions for energy-efficient watermarking in non-stationary signals, showing that the watermark's covariance should align with the host's covariance to resist linear attacks, extending known WSS results.

Contribution

It introduces a covariance-based condition for energy-efficient watermarking without assuming stationarity, generalizing existing WSS-based criteria.

Findings

Covariance matrix of watermark should be proportional to host covariance.

Results extend power spectrum conditions to non-stationary signals.

Provides geometric interpretation and simplified proof of main results.

Abstract

Energy efficient watermarking preserves the watermark energy after linear attack as much as possible. We consider in this letter non-stationary signal models and derive conditions for energy efficient watermarking under random vector model without WSS assumption. We find that the covariance matrix of the energy efficient watermark should be proportional to host covariance matrix to best resist the optimal linear removal attacks. In WSS process our result reduces to the well known power spectrum condition. Intuitive geometric interpretation of the results are also discussed which in turn also provide more simpler proof of the main results.