Roughness penalties on finite domains

Author

Sullivan, Joseph A O

Author_Institution

Dept. of Electr. Eng., Washington Univ., St. Louis, MO, USA

Volume

4

Issue

9

fYear

1995

fDate

9/1/1995 12:00:00 AM

Firstpage

1258

Lastpage

1268

Abstract

A class of penalty functions for use in estimation and image regularization is proposed. These penalty functions are defined for vectors whose indexes are locations in a finite lattice as the discrepancy between the vector and a shifted version of itself. After motivating this class of penalty functions, their relationship to Markov random field priors is explored. One of the penalty functions proposed, a divergence roughness penalty, is shown to be a discretization of a penalty proposed by Good and Gaskins (1971) for use in density estimation. One potential use in estimation problems is explored. An iterative algorithm that takes advantage of induced neighborhood structures is proposed and convergence of the algorithm is proven under specified conditions. Examples in emission tomographic imaging and radar imaging are given

Keywords

Markov processes; convergence of numerical methods; discrete systems; emission tomography; estimation theory; image processing; iterative methods; medical image processing; radar imaging; random processes; Markov random field priors; convergence; density estimation; discretization; divergence roughness penalty; emission tomographic imaging; estimation problems; finite domain; finite lattice; image regularization; induced neighborhood structures; iterative algorithm; penalty functions; radar imaging; Convergence; Gaussian processes; Helium; Image converters; Iterative algorithms; Lattices; Markov random fields; Radar imaging; Senior members; Tomography;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.413170

Filename

413170