A watermark is an invisible mark placed on an image that can be detected when the image is compared with the original. The mark is designed to identify both the source of an image as well as its intended recipient. The mark should be tolerant to reasonable quality lossy compression of the image using transform coding or vector quantization. Standard image processing operations such as low pass filtering, cropping, translation and rescaling should not remove the mark. Spread spectrum communication techniques and matrix transformations can be used together to design watermarks that are robust to tampering and are visually imperceptible. This paper discusses techniques for embedding such marks in grey scale digital images. It also proposes a novel phase based method of conveying the watermark information. In addition, the use of optimal detectors for watermark identification is also proposed

A watermark is an invisible mark placed on an image that is designed to identify both the source of an image as well as its intended recipient. The authors present an overview of watermarking techniques and demonstrate a solution to one of the key problems in image watermarking, namely how to hide robust invisible labels inside grey scale or colour digital images

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Index Terms-Escape rate, Nanomagnets, Reversal time of the magnetization, Spin-transfer torque.

The itinerant oscillator model describing rotation of a dipole about a fixed axis inside a cage formed by its surrounding polar molecules is revisited in the context of modeling the dielectric relaxation of a polar fluid via the Langevin equation. The dynamical properties of the model are studied by averaging the Langevin equations describing the complex orientational dynamics of two bodies (molecule-cage) over their realizations in phase space so that the problem reduces to solving a system of three index linear differential-recurrence relations for the statistical moments. These are then solved in the frequency domain using matrix continued fractions. The linear dielectric response is then evaluated for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio and along with the usual inertia corrected microwave Debye absorption gives rise to significant far-infrared absorption with a comb-like structure of harmonic peaks. The model may be also regarded as an extension of Budó's [J. Chem. Phys. 17, 686 (1949)] treatment of molecules containing rotating polar groups to include inertial effects.

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