Luigia Puccio

Multiwavelet analysis and signal processing

In this paper we present some results and applications concerning the recent theory of multiscaling 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 flexible schematization of the construction of semi-orthogonal multiwavelets. As in the scalar case, an efficient algorithm for the computation of the coefficients of a multiwavelet transform can be obtained, in which r input sequences are involved. This is a crucial point: the choice of a good prefilter which can provide a good approximation of the true initial coefficient 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 prefilter 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 different multiwavelet bases, and to test the effectiveness of multiwavelets in this kind of problem with respect to scalar wavelets.

Image compression through embedded multiwavelet transform coding

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.

Wavelet-based watermarking algorithms: theory, applications and critical aspects

The copyright protection of digital images is a critical element for multimedia applications on Web, electronic libraries and virtual image galleries. Since the middle of the nineties, digital watermarking techniques have been proposed as a streamlined solution to solve the copyright problem. In this article we present the difficulties occurred during the construction and the experimentation of our wavelet-based watermarking algorithm. In fact we faced the classical watermarking problems such as computational cost, imperceptibility and robustness. In addition to these critical aspects we had to resolve problems concerning the application of watermarking techniques on a real database Web gallery.

Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes

In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.

Tutela del diritto di proprieta'delle immagini digitali: Implementazione di un algoritmo di Watermark mediante funzioni Wavelet

Protection of copyright of the digital images is a critical element for the multimedia Web applications, e-books, virtual picture gallery. This problem is today receiving growing attention due to the pervasive diffusion of Internet technology. This work shows the watermark as solution to this problem and describes a new wavelet-based algorithm, called WM1.0, which is invisible, private, strong. WM1.0 watermaks a subset of digital images building the ecclesiastic on-line art collection. The Owner of the images and related information is the Italian Episcopal Conference, whereas the Publisher is I.D.S., an ICT company located in Messina.

Multiwavelets and Image Processing

This work contains a brief overview of the researches carried on by the authors on multiwavelet theory and applications. In particular, the effectiveness of multiwavelet techniques in image processing is shown and some evolutions of the theory are mentioned.

Fast resolution of integer Vandermonde systems

The resolution of polynomial interpolation problems with integer coefficients directly involves the open issue of the integer inversion of a general Vandermonde matrix defined over the field ℤ/p ℤ, for p prime number. The purpose of this paper is to demonstrate the possibility to invert a Vandermonde matrix with integer mod p coefficients and exactly compute the integer inverse matrix in the ring Mat(ℤ/p ℤ) of square matrices over ℤ/p ℤ through the new fast algorithm InVanderMOD. The explicit formula derived for the integer inversion of Vandermonde matrices entirely develops inside the field of the integers mod p , with due consideration to the operation of integer division. The inversion procedure InVanderMOD is valid for any prime number p and competitive in terms of computational effort, since its computational cost is less than O(n 3 ) .

A new approach of watermarking technique by means multichannel wavelet functions

The digital piracy involving images, music, movies, books, and so on, is a legal problem that has not found a solution. Therefore it becomes crucial to create and to develop methods and numerical algorithms in order to solve the copyright problems. In this paper we focus the attention on a new approach of watermarking technique applied to digital color images. Our aim is to describe the realized watermarking algorithm based on multichannel wavelet functions with multiplicity r = 3, called MCWM 1.0. We report a large experimentation and some important numerical results in order to show the robustness of the proposed algorithm to geometrical attacks.

Image-like surfaces: parallel least squares approximation methods

The “continuous-object discrete-image” model describing the general image restoration problem has been considered. Two different approaches for the parallelization of the regularized least squares method have been proposed, according to the two different available architectures: shared memory and distributed memory machines. The methods have been tested on a CRAY Y-MP/432 and an Intel iPSC/2, respectively, and timings and efficiency results have been given for several real images.

An Algorithm for LS - Colourations

An algorithm for L s - colourations of undirected graphs is described. This algorithm guarantees an optimal colouration and the correct value of the s-chromatic number for an arbitrary graph. Moreover, it can be used in case of directed graphs too.