Abstract

This paper describes an approach to reconstructing an optical object which has been subjected to low pass spatial-frequency filtering. The object is assumed to be of limited and known spatial extent and is further known to be non-negative and reasonably smooth. The smoothness constraint is incorporated into a regularizing matrix in a novel way. This matrix defines a regularized version of the original imaging equation, which is then solved using least-squares estimation under a non-negativity constraint. Combining constraints in this way can lead to reconstructions of very high quality.

© 1982 Optical Society of America

Least-squares reconstruction of objects with missing high-frequency components

C. K. Rushforth, A. E. Crawford, and Y. Zhou
J. Opt. Soc. Am. 72(2) 204-211 (1982)

Image restoration by an iterative damped least-squares method with non-negativity constraint

Junji Maeda
Appl. Opt. 24(6) 751-757 (1985)

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

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

Restoration of images with missing high-frequency components by minimizing the L₁ norm of the solution vector

Nabih N. Abdelmalek and Nobuyuki Otsu
Appl. Opt. 24(10) 1415-1420 (1985)

Restoration of images with missing high-frequency components using quadratic programming

Nabih N. Abdelmalek
Appl. Opt. 22(14) 2182-2188 (1983)