Image Restoration

Sanyukta Chetia
Assistant Professor
Deptt of ETC
JIST, Jorhat-10
Introduction
• Image enhancement is largely a subjective process, while image restoration is for
the most part an objective process
• Restoration attempts to recover an image that has been degraded by using a
priori knowledge of the degradation phenomenon. Thus, restoration techniques
are oriented toward modeling the degradation and applying the inverse process
in order to recover the original image
• This approach usually involves formulating a criterion of goodness that will yield
an optimal estimate of the desired result. By contrast, enhancement techniques
basically are heuristic procedures designed to manipulate an image in order to
take advantage of the psychophysical aspects of the human visual system. For
example, contrast stretching is considered an enhancement technique because it
is based primarily on the pleasing aspects it might present to the viewer, whereas
removal of image blur by applying a deblurring function is considered a
restoration technique
Contd..
• Some restoration techniques are best formulated in the spatial domain, while
others are better suited for the frequency domain
• For example, spatial processing is applicable when the only degradation is
additive noise. On the other hand, degradations such as image blur are difficult to
approach in the spatial domain using small filter masks. In this case, frequency
domain filters based on various criteria of optimality are the approaches of
choice. These filters also take into account the presence of noise
A Model of the Image Degradation/
Restoration Process
Contd..
• The degradation process is modeled as a degradation function that, together with an
additive noise term, operates on an input image f(x,y) to produce a degraded image
g(x,y)
• Given g(x,y), some knowledge about the degradation function H, and some knowledge
about the additive noise term the objective of restoration is to obtain an estimate 𝑓 ^ (x,y)
of the original image
• We want the estimate to be as close as possible to the original input image and, in
general, the more we know about H and η, the closer 𝑓 ^ (x,y) will be to f(x,y)
• If H is a linear, position-invariant process, then the degraded image is given in the spatial
domain by g(x,y) = h(x,y)*f(x,y)+η(x,y), where h(x,y) is the spatial representation of the
degradation function and * indicates convolution
• Convolution in the spatial domain is analogous to multiplication in the frequency
domain, so we may write the model equation in equivalent frequency domain
representation: G(u, v) = H(u, v)F(u, v) + N(u, v), where the terms in capital letters are the
Fourier transforms of the corresponding terms in the previous equation
Types of Image Degradations
• Noise: It is a disturbance that causes fluctuations in pixel values. Hence, pixel
values show random variations and this cannot be avoided. Thus, suitable
strategies should be designed to model and manage noise
• Blur: It is a degradation that makes an image less clear, thus making the process
of image analysis difficult. Some of the common blurs are Gaussian blur and
motion blur
• Artefacts: Distortions or artefacts are extreme intensity or colour fluctuations that
make an image meaningless. Distortions involve geometrical transformations
such as translation, rotation, or change in scale. In medical images, an artefact is
not a random noise. It is a spurious error or some systematic error that is present
in the image due to the faulty image-capturing process or due to the properties
of the image object. Artefact is a term that is mostly used in medical imaging
Noise Models
• The principal sources of noise in digital images arise during image acquisition
and/or transmission. The performance of imaging sensors is affected by a variety
of factors, such as environmental conditions during image acquisition, and by the
quality of the sensing elements themselves. For instance, in acquiring images
with a CCD camera, light levels and sensor temperature are major factors
affecting the amount of noise in the resulting image. Images are corrupted during
transmission principally due to interference in the channel used for transmission.
For example, an image transmitted using a wireless network might be corrupted
as a result of lightning or other atmospheric disturbance
Noise Types
• Based on distribution
• Based on correlation
• Based on nature
• Based on source
********** Refer to the pdf of noise types
Image Restoration Techniques
Based on the knowledge available for the degradation function, the following three
scenarios are possible:
Complete knowledge of the degradation function H is available. This is a simple
case in which an original image can be retrieved by applying an inverse filter. This
approach is called deconvolution (or inverse filtering)
Only partial knowledge of the degradation function H is available. A Weiner filter
is helpful in this scenario
There is no knowledge of the degradation function H. Approaches like blind
restoration techniques are used in this scenario.
Estimation of Degradation Functions
There are three principal ways to estimate the degradation function for use in
image restoration:
(1) observation,
(2) experimentation, and
(3) mathematical modeling
*************Refer to the pdf of estimation of degradation functions
Inverse Filter
•The simplest approach to restoration is direct inverse filtering
•It requires only the degradation function as a priori knowledge
•It produces perfect reconstruction in the absence of noise
•The inverse filtering approach makes no explicit provision for handling noise
•It is not always possible to obtain an inverse. For an inverse to exist, the matrix
should be non-singular
********Refer to the pdf of Inverse Filter
Wiener Filter
• Wiener filter incorporates both the degradation function and statistical
characteristics of noise into the restoration process
• It requires a prior knowledge of the power spectral density of original image
which is undesirable in practice
*********Refer to the pdf of Wiener Filter