Gianluca Vinti

In this paper, the connections between the Sampling Kantorovich model and the sampling process are highlighted and exploited. Based on the theoretical framework of the Sampling Kantorovich operators, a sampling paradigm, here named Sampling Kantorovich by Difference (SKD), is introduced. In line of principle, SKD allows for overcoming the technical limitation due to the fact that the resolution of a signal/image is strictly connected with the size of the used sensors. We analyze the paradigm in the case of a simulated super resolution type problem. The same mathematical model, being extendable to other signal reconstruction procedures, suggests a theoretical way for new technical solutions in the sampling procedures.

In this paper, we carry out a study developed on 13,677 images from 15 patients affected by moderate/severe atheromatous disease of the abdominal aortic tract. A procedure to extract the pervious lumen of the aorta artery from basal CT images is exploited and tested on a large scale. In particular, the above method takes advantage of the reconstruction and enhancing properties of the sampling Kantorovich algorithm which allows the information content of images to be increased. The processed image is compared, slice by slice, by superposition, with the corresponding contrast medium reference image. Numerical indices of errors were computed and analyzed in order to test the validity of the proposed method. The results achieved confirm, both from the numerical and clinical point of view, the good performance and accuracy of the proposed method, opening the possibility to perform an assisted diagnosis avoiding the injection of the contrast medium.