A constructive and unifying framework for zero-bit watermarking

In the watermark detection scenario, also known as zero-bit watermarking, a watermark, carrying no hidden message, is inserted in content. The watermark detector checks for the presence of this particular weak signal in content. The article looks at this problem from a classical detection theory point of view, but with side information enabled at the embedding side. This means that the watermark signal is a function of the host content. Our study is twofold. The first step is to design the best embedding function for a given detection function, and the best detection function for a given embedding function. This yields two conditions, which are mixed into one `fundamental' partial differential equation. It appears that many famous watermarking schemes are indeed solution to this `fundamental' equation. This study thus gives birth to a constructive framework unifying solutions, so far perceived as very different.Comment: submitted to IEEE Trans. on Information Forensics and Securit

Modelling galactic spectra: I - A dynamical model for NGC3258

In this paper we present a method to analyse absorption line spectra of a galaxy designed to determine the stellar dynamics and the stellar populations by a direct fit to the spectra. This paper is the first one to report on the application of the method to data. The modelling results in the knowledge of distribution functions that are sums of basis functions. The practical implementation of the method is discussed and a new type of basis functions is introduced. With this method, a dynamical model for NGC 3258 is constructed. This galaxy can be successfully modelled with a potential containing 30% dark matter within 1r_e with a mass of 1.6x10^11 M_o. The total mass within 2r_e is estimated as 5x10^11 M_o, containing 63% dark matter. The model is isotropic in the centre, is radially anisotropic between 0.2 and 2 kpc (0.88 r_e) and becomes tangentially anisotropic further on. The photometry reveals the presence of a dust disk near the centre

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local H\"older regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener integrals.Comment: 22 page

An Over-Massive Black Hole in the Compact Lenticular Galaxy NGC1277

All massive galaxies likely have supermassive black holes at their centers, and the masses of the black holes are known to correlate with properties of the host galaxy bulge component. Several explanations have been proposed for the existence of these locally-established empirical relationships; they include the non-causal, statistical process of galaxy-galaxy merging, direct feedback between the black hole and its host galaxy, or galaxy-galaxy merging and the subsequent violent relaxation and dissipation. The empirical scaling relations are thus important for distinguishing between various theoretical models of galaxy evolution, and they further form the basis for all black hole mass measurements at large distances. In particular, observations have shown that the mass of the black hole is typically 0.1% of the stellar bulge mass of the galaxy. The small galaxy NGC4486B currently has the largest published fraction of its mass in a black hole at 11%. Here we report observations of the stellar kinematics of NGC 1277, which is a compact, disky galaxy with a mass of 1.2 x 10^11 Msun. From the data, we determine that the mass of the central black hole is 1.7 x 10^10 Msun, or 59% its bulge mass. Five other compact galaxies have properties similar to NGC 1277 and therefore may also contain over-sized black holes. It is not yet known if these galaxies represent a tail of a distribution, or if disk-dominated galaxies fail to follow the normal black hole mass scaling relations.Comment: 7 pages. 6 figures. Nature. Animation at http://www.mpia.de/~bosch/blackholes.htm

Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging

Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging