Abstract

A linear mean-square estimator, optimum for image data available only on a finite interval, is derived for the restoration of images degraded by a system with a bandlimited spread function. The analysis is carried out in one dimension using a prolate-spheroidal-wavefunction expansion of the image data. When the noise is bandlimited to the same bandwidth as the spread function, the expansion represents the image data with zero mean-square error on the entire interval, and the mean-square reconstruction error is equal to that of the optimum linear estimate for image data on the infinite interval. The rate at which the series representation of the estimate converges is discussed and an example presented.

© 1969 Optical Society of America

Image Restoration by the Method of Least Squares

Carl W. Helstrom
J. Opt. Soc. Am. 57(3) 297-303 (1967)

Optical Spatial Filtering with the Least Mean-Square-Error Filter*

Joseph L. Horner
J. Opt. Soc. Am. 59(5) 553-558 (1969)

Degrees of Freedom of an Image

G. Toraldo di Francia
J. Opt. Soc. Am. 59(7) 799-804 (1969)

Restoration of bandlimited images by an iterative damped least-squares method with adaptive regularization

Junji Maeda
Appl. Opt. 24(10) 1421-1425 (1985)

Linear Restoration of Incoherently Radiating Objects

Carl W. Helstrom
J. Opt. Soc. Am. 62(3) 416-423 (1972)