Regularisation functions and estimators

Author

Nikolova, Mild

Author_Institution

Lab. des Signaux et Syst., CNRS, France

Volume

1

fYear

1996

fDate

16-19 Sep 1996

Firstpage

457

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 1996. Proceedings., International Conference on

Conference_Location

Lausanne

Print_ISBN

0-7803-3259-8

Type

conf

DOI

10.1109/ICIP.1996.560884

Filename

560884