Regularized Image Restoration

Abstract

In the previous chapter we have established the mathematical framework for image restoration by developing relevant models for both real-world images and the image formation process. The purpose of image restoration can now be formulated as the estimation of an improved image $\hat f$ of the original image f when a noisy blurred version g given by

$$ g = Df + \omega ,$$

((3.1))

is observed. In Chapters 3 through 5 we assume that the blurring matrix D is known. Further, some statistical knowledge about w and f is assumed to be available. Specifically, we will assume that the image model

$$ f = Af + v $$

(3.2)

is feasible. Methods to obtain the parameters of these models will be addressed in Chapters 6 through 8.