International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
Image Restoration Using
Wavelet based Image Fusion
Mohini Sharma1, Prof. Shilpa Datar2,
1
M. Tech Student, Dept. of Electronics & communication Engg., SATI, Vidisha, M.P., India
2
Asst. Prof., Electronics & Instrumentation Engg., SATI, Vidisha, M.P., India
Abstract- Image restoration is a field of image processing which
deals with restoring an image that has been degraded by some
degradation phenomenon. Degradation may occur due to motion
blur, Gaussian blur, noise or camera mismatch. This paper
presents a novel approach of image restoration based on image
fusion. In this work a motion blurred and noisy image is first
restored using Wiener and Lucy Richardson method. Wavelet
based Image fusion technique is then applied for restoration. It is
observed that image fusion technique provides better results as
compared to previous two techniques. Performance of all the
methods has been compared on the basis of performance
parameters MSE and PSNR.
Keywords- Image restoration, Image fusion, Wavelet, MSE,
PSNR, Wiener, Lucy Richardson.
I.INTRODUCTION
Restoration of digital images from their degraded model has
always been a problem of interest. A perfect solution to the
problem of image restoration is generally determined by
nature of degradation phenomena so it is highly dependent on
the nature of the noise present there.
A. Motion Blur
Blur can be caused by relative motion between the camera and
the original scene, by an out of focus of optical system,
atmospheric turbulences and aberrations in the optical system.
Variety of noise introduce by medium also cause degradation
and that results variation, distortion or shading in the original
image. So before further image processing we have to remove
the blur and reduce the amount of noise. Blur is a linear
convolution of an image with a blurring kernel, also known as
the PSF.
g(x, y) = f(x, y) * h(x, y) + v(x, y)
In this equation, h(x, y) is the blurring function, that is
convolved with the original image f(x, y) and v(x, y) is the
noise function, noise is additive Gaussian in nature. In order to
obtain the uncorrupted image, we need to find the blurring
function h(x, y). g(x, y) is the restored image.
B. Wiener Filter
It is linear image restoration named after Norbert Wiener, who
first proposed the method in 1942. It is also a non blind
method in which h(x, y) is known to us. The method
Considering image and noise as random processes and
objective is to find an estimate the uncorrupted image f such
ISSN: 2231-5381
that the mean square error between them should be minimized.
This error is given by
Where E is the expected value operator and f is the
undegraded image. It not only performs the deconvolution by
inverse filtering (high pass filter) but also removes the noise
with a compression operation (low pass filter).
H(u, v) = the degradation function
|H (u, v)|2 =H*(u, v) H(u, v)
H*(u, v) = the complex conjugate of H(u, v)
Sn (u, v) = |N(u, v)|2= the power spectrum of the noise
S(u, v) =|F(u ,v)|2= the power spectrum of the undegraded
image
C. Lucy Richardson Algorithm
The Lucy Richardson (LR) algorithm is an iterative nonlinear
restoration method maximizing the likelihood function of the
model yield an equation that is satisfied when following
iteration converges-
For best results number of iteration depends on the size and
complexity of the PSF matrix. Small PSF or few steps
sometime cause very smooth image and increasing numbers of
iteration slow down process but also produce ringing effect.
Thus for the “good” quality of reconstructed image, the
optimal no. of iterations are decided manually as per the PSF
size.
II.PROPOSED METHOD
Restoration techniques are basically mathematical modelling
of degradation and then applying inverse process to restore the
original image. In proposed method we compare Wiener filter,
Lucy richadson and wavelet based image fusion technique for
image restoration for removal of motion blur. Images restored
are compared on the basis of performance parameters like
PSNR and MSE.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
A. Image Restoration
Restoration is to reconstruct the original image with a priori
knowledge of the degradation. Degraded image is added with
noise and then given to restoration filter which suppress the
noise and the output which we get is near to the original image.
To remove blur Wiener and LR method is used as restoration
filters. Wiener is good with less complexity but LR provides
better PSNR than Wiener.
B. Block Diagram
Fig.1 shows the block diagram of the proposed method, in
first step noise is added with the original image. To remove
motion blur, in second step image is restored using restoration
algorithms that is Wiener (filter 1) and LR (filter 2). Finally
both Images are fused using image fusion method to get the
fused image in third step.
Fig.2 wavelet based image fusion
IV.EXPERIMENTAL RESULTS
The effect of restoration methods compares by two
performance parameterA.Mean Square Error (MSE)MSE= mean ((F(i, j)-R(i, j))^2)
B.Peak Signal to Noise Ratio (PSNR)PSNR= 10*log10 [(1^2)/MSE]
TABLE NO.1
COMPARISON OF PSNR FOR DIFFERENT IMAGE RESTORATION
METHODS
III.IMAGE FUSION
In image fusion the good information from each of the given
images is fused together to form a resultant image whose
quality is superior to the input source images. First DWT was
performed on the source image then images are decomposed
into four sub-bands LL, LH, HL, and HH. Then fused wavelet
coefficient map can be constructed from the wavelet
coefficients of the source images according to the fusion
decision map. The decision map shows each value which is
the index of source image, may be more informative on the
corresponding wavelet coefficient. Then, we will actually
make a decision on each coefficient. Mainly two type of
fusion rule are used first pixel- based so only pixel values
either max or average can consider and other is window-based
so consider not only the corresponding coefficients, but also
their close neighbours, say a 3x3 or 5x5 windows. We used
pixel level maxima rule in this work. On the basis of this
fusion decision map of source images, we can make the
wavelet coefficient map for fused image and then obtain the
fusion image by inverse wavelet transform.
ISSN: 2231-5381
Image
size
Wiener filter
(dB)
Lucy
Richardson(dB)
Wavelet
based image
fusion (dB)
For variance=0.05
256×256
15.868
19.43
19.447
512×512
20.197
20.768
20.834
For variance=0.005
256X256
23.805
24.098
25.377
512X512
26.808
28.759
29.002
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
TABLE NO.2
TABLE NO.4
COMPARISON OF MSE FOR DIFFERENT IMAGE RESTORATION
METHODS
COMPARISON OF PARAMETERS FOR FUSION USING DIFFERENT
WAVELETS
Image
size
Wiener filter
(dB)
Lucy
Richardson
(dB)
Wavelet
based image
fusion (dB)
Wavelet
Variance 0.005
Name
For variance=0.05
Lena.png 512x512
Lena.png 256x256
PSNR(dB)
MSE(dB)
PSNR(dB)
MSE(dB)
256X256
0.0259
0.0114
0.0113
HAAR
27.2914
0.0019
24.6875
0.0034
512×512
0.0095
0.0083
0.0082
SYM2
27.2491
0.0019
24.8615
0.0033
SYM4
27.6815
0.0017
24.8445
0.0033
SYM5
27.6374
0.0017
24.8467
0.0033
DB2
27.8020
0.0017
24.7933
0.0033
DB4
29.0936
0.0012
25.3334
0.0029
DB5
27.9033
0.0016
24.9247
0.0032
For variance=0.005
256X256
0.0042
0.0039
0.0029
512×512
0.0021
0.0013
0.0012
Table no.1 and Table no.2 shows all three methods of
restoration and comparison of that for different image size and
for variable variance in terms of PSNR (table no.1) and MSE
(table no.2).
TABLE NO.3
Fig.1TEST IMAGE LENA 512X512
COMPARISON OF PARAMETERS FOR FUSION USING DIFFERENT
WAVELETS
Wavelet
Name
Variance 0.05
Lena.png 512x512
Lena.png 256x256
PSNR(dB)
MSE(dB)
PSNR(dB)
MSE(dB)
HAAR
20.7025
0.0085
19.8493
0.0104
SYM2
20.8175
0.0083
19.4390
0.0114
SYM4
20.4616
0.0090
20.2342
0.0095
SYM5
20.1226
0.0097
20.0123
0.0100
DB2
20.9532
0.0080
20.2844
0.0094
DB4
21.4554
0.0072
20.5663
0.0088
DB5
20.6487
0.0086
20.1815
0.0096
Table no.3 and Table no.4 provides PSNR and MSE of image
fusion using different wavelets.DB4 gives best results
compare to all wavelets.
ISSN: 2231-5381
Fig.1 (a)Original image (b)Blurred image (c)Image restored by wiener filter
(d)Image restored by Lucy richardson (e)Image restored by fusion (max).
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
REFERENCES
Fig.2 TEST IMAGE LENA 256X256
Fig.2 (a)Original image (b)Blurred image (c)Image restored by wiener filter
(d)Image restored by Lucy Richardson (e)Image restored by fusion (max).
V.CONCLUSION
This paper compares three methods of restoration for removal
of motion blur. Blurred image is restored using Wiener filter
method and Lucy Richardson method. The results based on
Lucy Richardson provided better results than Wiener filter
method. Then a third method of Wavelet based image fusion
is used to achieve higher PSNR and minimum MSE as
compared to other two techniques. For the further work the
performance of this method can be compared with the other
fusion algorithms like edge based fusion and region based
fusion.
ISSN: 2231-5381
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