In2414961500

Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1496-1500
Amputation of Motion Blur From Photograph Using Iterative
Approach in Frequency Domain
Ashish Jain [1], Prof. Delkeshwar Pandey [2]
[1]
Department of Computer Science & Engineering, U.P. Tech. University, Lucknow, INDIA
[2]
Department of Computer Science & Engineering, U.P. Tech. University, Lucknow, INDIA

ABSTRACT
In current years blur removing techniques in approximately described by this equation:
the presence of noise have become a great deal of
attention in the field of image processing under image g = PSF*f + N,
restoration [7], [1]. There are several approaches to
image denoising, which include linear filters, Where: g the blurred image, h the distortion
nonlinear filters and Fourier / Wavelet transforms. operator called Point Spread Function (PSF), f the
Image denoising problem is equivalent to that of original true image and N Additive noise, introduced
image restoration when blurs are not included in the during image acquisition, that corrupts the
noisy image .Image restoration is the process of image[8].Image deblurring is an inverse problem
recovering the original image from the degraded which is used to recover an image which has suffered
image and also understand the image without any from linear degradation. The blurring degradation can
artifacts errors. Image restoration methods can be be space-invariant or space-in variant [6]. Image
considered as direct techniques when their results are deblurring methods can be divided into two classes:
produced in a simple one step fashion. Equivalently, nonblind, in which the blurring operator is known
indirect techniques can be considered as those in and blind, in which the blurring operator is unknown.
which restoration results are obtained after a number
of iterations. Iterative techniques such as iterative 1.2 Iterative Image Deblurring Techniques
Wiener Filtering [5], [3] can be considered as simple i). Iterative Wiener Filter Deblurring Technique-The
indirect restoration techniques. The problem with Wiener filter isolates lines in a noisy image by
such methods is that they require knowledge of the finding an optimal tradeoff between inverse filtering
blur function that is point -spread function (PSF) and and noise smoothing. It removes the additive noise
estimation of power spectrum which is, usually not and inverts the blurring simultaneously so as to
available when dealing with image blurring. In this emphasize any lines which are hidden in the image.
paper Iterative approach in frequency domain using This filter operates in the Fourier domain [3], making
Blind deconvolution approach, for image restoration the elimination of noise easier as the high and low
is discussed, which is the recovery of a sharp version frequencies are removed from the noise to leave a
of a blurred image. sharp image. The Wiener filter in Fourier domain can
be expressed as follows:
Keywords: Blind Deconvolution, Degradation
Model, Frequency Domain, Iterative Approach,
Image Restoration, PSF

1. INTRODUCTION
Blurring is a form of bandwidth reduction of Where Sxx(f1,f2),Snn(f1,f2) are power spectra
the image due to imperfect image formation process. of original image and additive noise and H(f1,f2) is
It can be caused by relative motion between camera blurring filter.
and original images. Normally, an image can be An iterative procedure for wiener filter in
degraded using low-pass filters and its noise. This spatial domain is listed below:
low-pass filter is used to blur/smooth the image using 0. Initialization: Rf (0) =Rg, where Rg is the the
certain functions. In digital image there are 3 autocorrelation matrix of g1. Wiener filter
common types of Blur effects: Average Blur, construction: B(i+1) =Rf(i)HH[ HR f(i) HH +Rn]−1
Gaussian Blur and Motion Blur. Image deblurring 2. Restoration: ˜f (i+1) =B(i+1)g
can performed for better looking image, improved 3. Update: Rf (i+1) =E{˜f(i+1) ˜f (i+1)}
identification, PSF calibration, higher resolution and Steps 1 to 3 are repeated until the result converges.
better quantitative Analysis. The iterative Wiener filter in discrete Fourier domain
is given as:
1.1 Deblurring Model pg p2 f i ph 2
𝑝𝑓 i + 1 =
A blurred or degraded image can be [𝑝 𝑓 i ph 2 + pn ]2

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The problem with this method is that they like edges which have been degraded by noise.
require knowledge of the blur function that is point Results are evaluated and compared based on
spread function (PSF) and estimation of power Evaluation Metrics Mean Square Error [MSE] and
spectrum. Signal-to-Noise Ratio [SNR]. Fig.1 shows a block
ii). Additive iterative algorithm-The questions are diagram of our method.
whether the estimate of the power spectral density
converges, and whether it converges to the true value. 2.1 Blind Deconvolution approach
It is easy to prove that pf (i) is sure to converge to Blind Deconvolution is a subset of Iterative
some value ˜pf, because pf (i) as a sequence is both Constrained algorithms which produce an estimate of
monotonic (The derivative of pf (i+1) with respect to h(x) concurrently with f(x) [2], [4]. It does not need
pf(i) is greater than 0 and bounded. ˜p f can be derived the PSF h(x) to be measured. Other iterative
as follows: constrained algorithms require h(x) to be measured
by acquiring data from sub resolution fluorescent
1 pn 3p 2 n 2p n p f beads.
˜pf = [˜pf − ± p2 f − −
2 ph 2 ph 4 ph 2 g(x) = f(x)*h(x)+n(x)
Where g(x): measurement, f(x): unknown object,
The problem is that ˜pf does not converge to h(x): unknown or poorly known PSF, n(x):
pf unless 𝑝 𝑛 is 0. So a correction item is added in contamination
every iteration, and an additive iterative method was
put forward. 𝑝∗ 𝑓 is used as the update of original 2.2 Blurring Parameter
image instead of pf. It can be derived that The parameters needed for blurring an
image are PSF, Blur length, Blur angle and type of
𝑝∗ 𝑓 i + 1 = 𝑝∗ 𝑓 i noise. Point Spread Function is a blurring function.
2 ∗ 2 2 ∗ 2 When the intensity of the observed point image is
ph 𝑝 𝑓 i [ ph 𝑝 𝑓 i − pn ]
+ spread over several pixels, this is known as PSF. Blur
[𝑝∗ 𝑓
i ph 2 + p ]2
n length is the number of pixels by which the image is
degraded. It is number of pixel position is shifted
2. PROPOSED ALGORITHM from original position. Blur angle is an angle at
(ERADICATOR) FOR AMPUTATION OF which the image is degraded. Available types of
MOTION BLUR noise are Gaussian noise, salt and pepper noise,
The method proposed in this paper reduces Poisson noise, Speckle noise which is used for
the noise in the image restored by Iterative approach blurring. In this paper, we are using Gaussian noise
using the Blind deconvolution with different blur which is also known as white noise. It requires mean
parameters like length and blur angle. Proposed and variance as parameters.
algorithm is to reconstruct frequency components

2.3 Architecture of image degradation and
amputation of motion blur
Fig.1 illustrate that the original image is degraded or
blurred using degradation model to produce the
blurred image. The blurred image should be an input
to the deblurring algorithm. Various algorithms are
available for deblurring. In this paper, we are going
to use blind deconvolution algorithm. The result of
this algorithm produces the deblurring image which
can be compared with our original image.

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Input Image

Degrade Image

By Adding

Blurring (Motion Blur) Noise

Identify Motions by
Estimation of PSF Noise models (probability density functions)
(based on length and
theta)
Impulse Gaussian Poisson Speckle

Amputation of motion blur
(Without noise)

Inverse filtering Amputation of noise by algorithms
(in frequency domain)

Iterative Wiener Proposed algorithm
filtering (Eradicator)

Fig.1 Block diagram of image degradation and amputation of motion blur with and without noise

3. PROPOSED ALGORITHM simultaneously. Instead of computing the desired
(ERADICATOR) (deblurred) image directly, our method computes a
Proposed Algorithm (Eradicator) can be sequence of images, which converges to the desired
used effectively when no information of distortion image. Our algorithm is based on the following
is known; it restores image and PSF steps:
𝑔
Step 1: First assume that ˜fo use a positive constant Øn = ˜h
ⱷ𝑛
image with a constant value equal to average of the 𝑔
Where “ ” denotes pixel by pixel division.
blurred image. ⱷ𝑛
Step 2: This step of the iteration performs a Assume, if some pixel values of ⱷ𝑛 = 0 , then we
convolution of the current assumption with the get 𝑔/ⱷ𝑛 = 0.
PSF: Step 4: At the final step, a new assumption is the
ⱷn = h ˜fn product of the current one and the correction factor
Step 3: In this step compute a correction factor :
based on the result of the last operation and the ˜fn+1 = ˜fn . Øn ,
original (degraded) image: Where “ . ” is the pixel by pixel multiplication.

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4. SAMPLE RESULTS
The below images Fig.2 represents the result of proposed algorithm. The sample image after applying
the proposed algorithm will be as follows.

Blured image with Image after 20th Image after 40th Image after 60th Image after 80th
Noise iterations iterations iterations iterations

Image after 100th Image after 120th Image after 140th Image after 160th Image after 180th
iterations iterations iterations iterations iterations
Fig.2 Results of the proposed algorithm (Eradicator) for image deblur

7.00E+03

6.00E+03

5.00E+03

4.00E+03
MSE

3.00E+03 IWF

2.00E+03 PA

1.00E+03

0.00E+00
20 40 60 80 100 120 140 160 180

No. of Iterations

Fig.3 Graph of MSE for comparison of Iterative wiener filter (IWF) and proposed algorithm (PA)

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20

15

PSNR 10
IWF
5 pa

0
20 40 60 80 100 120 140 160 180

No. of Iterations

Fig.4 Graph of PSNR for comparison of Iterative wiener filter (IWF) and proposed algorithm (PA)

No. of Iterations IWF PA deblurring images proposed algorithm (pa) is used
and the deblurred images obtained are shown in
20 1.92E+03 986.6066 fig.2.Performance measure values obtained are
40 2.36E+03 1.42E+03 shown in table 1 and table 2.
60 3.66E+03 1.75E+03
5. CONCLUSION
80 3.89E+03 2.01E+03 We have presented a method for Iterative
100 4.56E+03 2.24E+03 blind image deblurring. The method differs from
120 5.23E+03 2.43E+03 most other existing methods by only imposing
weak restrictions on the blurring filter, being able
140 6.21E+03 2.61E+03 to recover images which have suffered a wide
160 6.68E+03 2.78E+03 range of degradations. Good estimates of both the
180 6.98E+03 2.93E+03 image and the blurring operator are reached by
initially considering the main image edges. The
restoration quality of our method was visually and
Table 1: MSE Performance measure values
quantitatively better than those of the other
for values for IWF and proposed algorithm
algorithms. The advantage of our proposed
algorithm (Eradicator) is used to deblur the
No. of Iterations IWF pa degraded image without prior knowledge of PSF
20 15.2927 18.1894 and estimation of power spectrum.
40 1.08E+01 16.6177
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image deconvolution, “IEEE sig. process.
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Table 2: PSNR Performance measure valuesfor Restoration via Wiener Filtering in the
values for IWF and proposed algorithm Frequency Domain” wseas transactions on
signal processing Issue 2, Volume 5, pp.
From Fig.3 and Fig.4 it can conclude that 63-73 February 2009.
the proposed algorithm (pa) gives better results as [4] Jain-feng cai, hui ji, Chaoqiang lie,
compare to the iterative wiener filter (IWF). So for Zuowei Shen., “blind Motion deblurring

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using multiple images”. Journal of on image processing, Vol 17, pp.105-116,
Computation Physics. Pp. 5057-5071, No. 2 Febreary 2008.
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[6] Michal Sorel and Jan Flusser, Senior [8] Salem Saleh Al-amri et. al. “A
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