The aim of this paper is to provide a theoretical set up and a mathematical model for the problem of image reconstruction. The original image belongs to a family of two-dimensional (2-D) possibly discontinuous functions, but is blurred by a Gaussian point spread function introduced by the measurement device. In addition, the blurred image is corrupted by an additive noise. We propose a preprocessing of data which enhances the contribution of the signal discontinuous component over that one of the regular part, while damping down the effect of noise. In particular we suggest to convolute data with a kernel defined as the second order derivative of a Gaussian spread function. Finally, the image reconstruction is embedded in an optimal problem framework. Now convexity and compactness properties for the admissible set play a fundamental role. We provide an instance of a class of admissible sets which is relevant from an application point of view while featuring the desired properties
A BAYESIAN APPROACH TO EDGE DETECTION IN BLURRED NOISY IMAGES / DE SANTIS, Alberto; Sinisgalli, C.. - In: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I. FUNDAMENTAL THEORY AND APPLICATIONS. - ISSN 1057-7122. - STAMPA. - 46:6(1999), pp. 686-699. [10.1109/81.768825]
A BAYESIAN APPROACH TO EDGE DETECTION IN BLURRED NOISY IMAGES
DE SANTIS, Alberto;
1999
Abstract
The aim of this paper is to provide a theoretical set up and a mathematical model for the problem of image reconstruction. The original image belongs to a family of two-dimensional (2-D) possibly discontinuous functions, but is blurred by a Gaussian point spread function introduced by the measurement device. In addition, the blurred image is corrupted by an additive noise. We propose a preprocessing of data which enhances the contribution of the signal discontinuous component over that one of the regular part, while damping down the effect of noise. In particular we suggest to convolute data with a kernel defined as the second order derivative of a Gaussian spread function. Finally, the image reconstruction is embedded in an optimal problem framework. Now convexity and compactness properties for the admissible set play a fundamental role. We provide an instance of a class of admissible sets which is relevant from an application point of view while featuring the desired propertiesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
