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

A semi-coherent analysis method to search for continuous gravitational waves emitted by ultra-light boson clouds around spinning black holes

As a consequence of superradiant instability induced in Kerr black holes, ultra-light boson clouds can be a source of persistent gravitational waves, potentially detectable by current and future gravitational-wave detectors. These signals have been predicted to be nearly monochromatic, with a small steady frequency increase (spin-up), but given the several assumptions and simplifications done at theoretical level, it is wise to consider, from the data analysis point of view, a broader class of gravitational signals in which the phase (or the frequency) slightly wander in time. Also other types of sources, e.g. neutron stars in which a torque balance equilibrium exists between matter accretion and emission of persistent gravitational waves, would fit in this category. In this paper we present a robust and computationally cheap analysis pipeline devoted to the search of such kind of signals. We provide a full characterization of the method, through both a theoretical sensitivity estimation and through the analysis of syntethic data in which simulated signals have been injected. The search setup for both all-sky searches and higher sensitivity directed searches is discussed.Comment: 13 pages, 13 figure

Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution.Comment: 11 pages, 6 figures, accepted for publication in IEEE transactions on information theor

Roadmap on optical security

Postprint (author's final draft