# Un sistema interattivo grafico per l'elaborazione di segnali

Puccio, Luigia and Lazzaro, Damiana (1989) Un sistema interattivo grafico per l'elaborazione di segnali. Accademia Peloritana dei Pericolanti Classe FF.MM.NN., 67. pp. 195-231.

 PDF atti_3_1989_195.pdf Restricted to users from Unime Download (7MB) | Request a copy

## Abstract

In this work a package of algorithrns, for digital image processing, and the interactive mani program are decribed. Principally, this interactive system with graphical facilities, made for a Wòrk-station MicroVAX/GPX, is oriented to the one-dimensional case (digital signal processing) to soive the «signal restoration problem». It is well known that the linear model describing the image restoration problem is given by a Fredholm integral equation of the first kind that is an ill-posed problem. Since, in this case, the data are measured quantities, measurement errors can be magnified by instabilities in the computed solution. In order to avoid these instabilities «regularization methods» have been deveioped. These methods depend on a smail positive parameter, $\gamma$, and on a regularizing operator. The choice of the regularization parameter $\gamma$ is cruciai to effectively apply the method. In fact, it controls the amount of smoothing of the regularized solution and must guarantee the convergence of that solution to the Fredholm integrai equation solution. We have used the interactive program: (1) to study a polynomiai regularizing operator for the spaces of spline of degree 3 and smoothness class k (with k = 1, 2) and the space of smooth linear spline, where the approximate solution of the problem has been calculated; (2) to analyse whether, in this cases, it is possible to use the «discrepancy condition» for the choice of the optimal regularization parameter . We present some numerical results, where the discrepancy condition helps to find the optimum regularization parameter $\gamma$ which gives an approximate solution for the <<signal restoration problem>>

Item Type: Article M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1989M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Medico-Biologiche > 1989M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1989M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere, Filosofia e belle Arti > 1989 Dr M P 05 Oct 2012 07:33 22 Jan 2013 11:10 http://cab.unime.it/mus/id/eprint/934