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This paper presents a digital color image watermarking scheme using the hypercomplex numbers representation and the Quaternion Fourier Transform (QFT). Previous color image watermarking methods are first presented and the quaternion representation is then described. In this framework RGB pixel values are associated with an unique quaternion number having three imaginary parts. The QFT is presented, this transform depends on an arbitrary unit pure quaternion. The value of is selected to provide embedding spaces having robustness and/or perceptual properties. In the presented approach is function of the mean color value of a block and a perceptual component. A watermarking scheme based on the QFT and the Quantization Index Modulation scheme is afterwards presented. This scheme is finally evaluated for different color image filtering process (JPEG, blur) and the fact that perceptive QFT embedding can offer robustness to luminance filtering techniques is outlined.

International audienceIn this paper, we use a biquaternion formalism to model vector-sensor signals carrying polarization information. This allows a concise and elegant way of handling signals with eight-dimensional (8-D) vector-valued samples. Using this model, we derive a biquaternionic version of the well-known array processing MUSIC algorithm, and we show its superiority to classically used long-vector approach. New results on biquaternion valued matrix spectral analysis are presented. Of particular interest for the biquaternion MUSIC (BQ-MUSIC) algorithm is the decomposition of the spectral matrix of the data into orthogonal subspaces. We propose an effective algorithm to compute such an orthogonal decomposition of the observation space via the eigenvalue decomposition (EVD) of a Hermitian biquaternionic matrix by means of a newly defined quantity, the quaternion adjoint matrix. The BQ-MUSIC estimator is derived and simulation results illustrate its performances compared with two other approaches in polarized antenna processing (LV-MUSIC and PSA-MUSIC). The proposed algorithm is shown to be superior in several aspects to the existing approaches. Compared with LV-MUSIC, the BQ-MUSIC algorithm is more robust to modelization errors and coherent noise while it can detect less sources. In comparaison with PSA-MUSIC, our approach exhibits more accurate estimation of direction of arrival (DOA) for a small number of sources, while keeping the polarization information accessible

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[1] Rayleigh wave ellipticity as a function of frequency is closely linked to underground structure, i.e., shear wave velocity profile and sediment thickness. The possibility to calculate these underground properties by inverting ellipticity curves has recently been shown. We propose a new technique enabling the Rayleigh wave ellipticity to be recovered over a wide frequency range by using ambient noise recordings. Based on the random decrement technique commonly used to characterize dynamic parameters of buildings, this method eliminates all wave types except Rayleigh waves. We apply the method to noise synthetics simulated for different underground structures and show its applicability to real seismic noise data. Citation: Hobiger, M., P.-Y. Bard, C. Cornou, and N. Le Bihan (2009), Single station determination of Rayleigh wave ellipticity by using the random decrement technique

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