539
12
Image Restoration
The concept of image restoration differs substantially from the idea
of image enhancement. While enhancement aims at improving the
appearance of the image or its properties with respect to the follow
ing analysis (by a human operator or even automatic), the goal of
restoration is to remove an identified distortion from the observed
image
g
, thus providing (in a defined sense) the best possible esti
mate
of the original undistorted image
f
. The observed image may
be distorted by blur, geometrical deformation, nonlinear contrast
transfer, etc., and is usually further degraded by additive or other
wise related noise
. The identification of the properties of distortion
(i.e., of the distorting system, the disturbing noise, etc.) therefore
forms an essential part of the restoration process. Having described
the distortion formally by a mathematical model with measured or
estimated parameters, we can try to invert the model and obtain the
restored image (estimate of the original) as the result of applying
the inverse procedure to the observed (measured, received) image.
The schematic representation of the distortion and restoration pro
cess is depicted in
Figure 12.1.
f
© 2006 by Taylor & Francis Group, LLC
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
540
Jan
The images may be distorted in many directions. In this chap
ter, we shall deal primarily with the following types of distortion,
which cover most of those met in practice:
•
Intensity distortion, global or space variable
•
Geometrical distortion
•
Blur, e.g., due to defocus or motion
•
Interference by noise of certain properties
The methods of identification of distortion models and param
eters are specific to individual types of distortion. Therefore, the
identification will be discussed in the individual sections, usually
before the actual methods of restoration.
Basically, two approaches are used in restoration. The concep
tually simpler of them means formulating distortion models that can
be directly inverted (as, e.g., for purely linear distortion); solving the
equation systems or using closed formulae obtained by the inversion
then provides straightforwardly the estimate of the original. When
noise cannot be neglected, the exact inversion is impossible, as the
noise represents an unknown stochastic component. In these cases,
an approximate inversion minimizing the noise inﬂuence must be
sought; the commonly used approach is the least mean square (LMS)
error approach, which may lead to closed formulae as well (e.g.,
Wiener type filtering). Often, however, the realistic distortion models
are so complex (structurally and/or mathematically) that the direct
inversion is not feasible or suffers with too high errors. In such a
case, the way that proved successful is gradual optimization aiming
at an extreme of a criterion function derived from the distortion
model. The rich body of optimization theory and iterative algorithms
combined with the signaltheoretical concepts thus provide a powerful
tool that often enables the recovering of useful information even from
heavily distorted images. Different concepts of this kind will be brieﬂy
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 Singh
 Image processing, Signal Processing, The Land, Inverse function, Francis Group, Taylor & Francis Group

Click to edit the document details