Spread spectrum image watermark detection on degraded compressed sensing measurements with distortion minimization

Abstract

In the age of digital world, the wide dissemination of images need bandwidth (BW) efficient transmission as well as ownership protection during transmission over radio mobile channel. Compressed sensing (CS) nowadays finds a potential application for BW efficient transmission over wireless network while digital watermarking, more specifically, spread spectrum (SS) watermarking is found to be efficient for copyright protection. To this aim, an SS watermarking scheme on CS images is proposed in presence of both multiplicative and additive impairments that support a general framework of radio mobile channel. First a mathematical form of watermark detection threshold in log-likelihood ratio model is derived followed by an optimization framework to minimize the visual distortion that includes CS reconstruction and watermark embedding distortion while satisfying some certain detection reliability constraints. An approximate closed form solution to the optimization problem in terms of embedding strength and a set of appropriate host samples selection for a given number of CS measurements is derived. A large set of simulation results on Rayleigh distribution as multiplicative degradation and Gaussian distribution as additive noise are reported. Performance comparison with the existing works validate the efficacy of the proposed method in terms of imperceptibility and improved detection reliability against a large set of diverse signal processing operations.