In digital management, multimedia content and data can easily be used in an illegal way-being copied, modified and distributed again. Copyright protection, intellectual and material rights protection for authors, owners, buyers, distributors and the authenticity of content are crucial factors in solving an urgent and real problem. In such scenario digital watermark techniques are emerging as a valid solution. In this paper, we describe an algorithm-called WM2.0-for an invisible watermark: private, strong, waveletbased and developed for digital images protection and authenticity. Using discrete wavelet transform (DWT) is motivated by good time-frequency features and well-matching with human visual system directives. These two combined elements are important in building an invisible and robust watermark. WM2.0 works on a dual scheme: watermark embedding and watermark detection. The watermark is embedded into high frequency DWT components of a specific sub-image and it is calculated in correlation with the image features and statistic properties. Watermark detection applies a re-synchronization between the original and watermarked image. The correlation between the watermarked DWT coefficients and the watermark signal is calculated according to the Neyman-Pearson statistic criterion. Experimentation on a large set of different images has shown to be resistant against geometric, filtering and StirMark attacks with a low rate of false alarm. Published by Elsevier B.V. MSC: 65T60; 65Y99; 68U10; 94A08; 94A62

The growth of the Internet has increased the phenomenon of digital piracy, in multimedia objects, like software, image, video, audio and text. Therefore it is strategic to individualize and to develop methods and numerical algorithms, which are stable and have low computational cost, that will allow us to find a solution to these problems. We describe a digital watermarking algorithm for color image protection and authenticity: robust, not blind, and wavelet-based. The use of Discrete Wavelet Transform is motivated by good time-frequency features and a good match with Human Visual System directives. These two combined elements are important for building an invisible and robust watermark. Moreover our algorithm can work with any image, thanks to the step of pre-processing of the image that includes resize techniques that adapt to the size of the original image for Wavelet transform. The watermark signal is calculated in correlation with the image features and statistic properties. In the detection step we apply a resynchronization between the original and watermarked image according to the Neyman-Pearson statistic criterion. Experimentation on a large set of different images has been shown to be resistant against geometric, filtering, and StirMark attacks with a low rate of false alarm.

We provide the theoretical results for the construction of special classes of biorthogonal multivariate wavelet systems. In particular, by making use of the parameterization given by the lifting scheme, we show how certain properties of the filters, which are desirable in many applications, can be reproduced, namely symmetry with respect to some symmetry group and sum rules/vanishing moments conditions.