In this work we present some results and applications concerning the recent theory of multi-scaling functions and multiwavelets. In particular, we present the theory in compact notation with the use of some types of recursive block matrices. This allows a exible schematization of the construction of semi-orthogonal multiwavelets. As in the scalar case, an e cient algorithm for the computation of the coe cients of a multiwavelet transform can be obtained, in which r input sequences are involved. This is a crucial point: the choice of a good pre lter which can provide a good approximation of the true initial coe cient sequences, when applied to the input data, is critical in the context of multiwavelet analysis. We explore this problem with concrete examples, showing the strong dependence of the pre lter on the chosen multiwavelet basis. Finally, an application of the multiwavelet-based algorithm to signal compression is shown. The goal is both to compare the results obtained with di erent multiwavelet bases, and to test the e ectiveness of multiwavelets in this kind of problem with respect to scalar wavelets.

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

In this paper, multiwavelets are considered in the context of image compression and two orthonormal multiwavelet bases are experimented, each used in connection with its proper prefilter. For evaluating the effectiveness of multiwavelet transform for coding images at low bit-rates, an efficient embedded coding of multiwavelet coefficients has been realized. The performance of this multiwavelet-based coder is compared with the results obtained for scalar wavelets.

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