Title :
Regularisation functions and estimators
Author_Institution :
Lab. des Signaux et Syst., CNRS, France
Abstract :
We characterise the features of a regularised ML estimate, or equivalently a MAP estimate, of an image (or a signal) in relation with the form of the regularisation. The unknown image (signal) is observed through a linear operator and the data are corrupted by white Gaussian noise. Its reconstruction is regularised by the energy of a first-order Markov random field where the contributions of the transitions between adjacent neighbours are weighted using general potential functions (PFs). We exhibit the relationship between several features of the estimate and the form of the PF. Points of interest are the edge recovery, the stability of the estimator, the estimation of locally constant regions, the bias over large transitions, the resolution. The exposed theoretical considerations are corroborated by numerical simulations
Keywords :
Gaussian noise; Markov processes; edge detection; image reconstruction; image resolution; image segmentation; maximum likelihood estimation; random processes; white noise; MAP estimate; bias; edge detection; edge preservation; edge recovery; estimator stability; first-order Markov random field; general potential functions; image reconstruction; image resolution; linear operator; locally constant regions; numerical simulations; regularisation estimators; regularisation functions; regularised ML estimate; signal reconstruction; transitions; white Gaussian noise; Bayesian methods; Ear; Gaussian noise; Image edge detection; Image reconstruction; Markov random fields; Maximum likelihood estimation; Numerical simulation; Signal resolution; Stability;
Conference_Titel :
Image Processing, 1996. Proceedings., International Conference on
Conference_Location :
Lausanne
Print_ISBN :
0-7803-3259-8
DOI :
10.1109/ICIP.1996.560884
