Iterative methods for image deblurring

TLDR

Iterative restoration algorithms are used to remove linear blurs and nonlinear degradations from photographic images, incorporating prior knowledge, handling nonstationary blurs, and being robust to blurring‑operator errors, while classical solutions such as inverse, Wiener, and constrained least‑squares filters are limiting cases of these iterations. The study introduces regularization to prevent excessive noise magnification in ill‑conditioned deblurring problems. It shows that terminating the algorithms after a finite number of iterations minimizes noise effects.

Abstract

The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed.