Jun 16 • Notes • 3877 Views • 1 Comment on IMAGE RESTORATION


  1. Image restoration is use to improve the appearance of an image.
  2. Restoration technique on image degradation tends to be based on mathematical or probabilistic model so, it is objective.



Input image is f(x, y) and this image is degraded by degradation function H(x, y) and we have noise h(x, y) and the noise is present during channel transmission. It gives

g(x, y) = h(x,y) * f(x, y) + Ƞ(x, y)

frequency domain representation is given by

G(u, v) = H(u, v) F(u, v) + N(u, v)


During the image acquisition or transmission principal source of noise in digital image is arises. Environmental condition during image acquisition and the quality of sensing elements effects the performance of imaging sensor.



  1. Ideal band reject filter

H(u, v) =  1, D0 + W/2 < D(u, v)< D0 – W/2

0, D0 – W/2 < D(u, v) < D0 + W/2

Where W is width of band.

i.Butterworth band reject filter

H(u, v) = 1/ 1+ [D(u, v)W/D2(u, v)-D02]2n

ii.Gaussian band reject filter

H(u,v) = 1- e-1/2[D2(u, v)-D02/ D(u, v)W]  

 Band pass filter

Hbp(u, v) = 1- Hbr(u, v)

Estimation of degradation function-

Degradation function can be estimated by three principle way in image restoration and  these are

  • Observation
  • Experimentation
  • Mathematical modeling

Inverse filtering

Blur and the noise is removed from the image and the process of removing is known as inverse filtering or it is also known as deconvolution. It is a constrained method of image restoration technique. Here we take an assumption that a blur is characterized by the impulse response of the system or point spread function(PSF). And also we assumes that blurs are linear and image system is convolution of the impulse.

Wiener filter

It is an optimal filter. It restores the images and also by image smoothing noise is removed. To design a wiener filter we required an estimation of original and additive noise. And it is a unconstrained method of image restoration technique.


It is a process of approximation of many types of degradation. Advantage of the process is

  • Image restoration problems can be solved by the use of extensive tools of linear system theory.
  • Position dependent technique are usually more accurate


  • It mainly uses two transforms
  1. Radon transform
  2. Fourier transform

For example computed tomography(CT) uses this transform and it is an important medical imaging technique.

Two types of projection are-

  1. Back projection
  • It is a starting point and a sigle projection is not able to carry enough information image reconstruction.
  • Along the direction from which the beam came project the 1D signal .

2.  Multiple projection

  • From multiple direction sum sum of the back projection is multiple projection.
  • This projection gives the idea about the image we are reconstructing.


  1. What is image restoration??

ANSWER-Image restoration is use to improve the appearance of an image.Image restoration technique on image degradation tend to be based on mathematical or probabilistic models so, it is objective.

2.Which of the noise may present in the degradation of an imge??

ANSWER-There are seven noises which effects are

  1. Guassian noise
  2. Rayleigh noise
  3. Erlange noise
  4. Exponential noise
  5. Uniform noise
  6. Periodic noise
  7. Impulse noise                                                                                                                          3.What are the two methods of image restoration??

ANSWER-Two methods of image restoration are

  1. Constrained method
  2. Unconstrained method                                                                                                                                                                                4.What are the transforms for image reconstruction from projection??

ANSWER-There are two transforms and these are

  1. Radon transform
  2. Fourier transform

GATE Syllabus-

1.Gate syllabus for Electronics and Communication 2014

IES Syllabus-

1.IES Syllabus for Electronics and telecommunication 

2. IES Syllabus for General Ability








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  1. Dinesh says:

    This article is neatly aligned and cleanly explained the concept about the image restoration…

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