1. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 4, July-August (2013), © IAEME
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IMAGE RESOLUTION ENHANCEMENT BY USING WAVELET
TRANSFORM
Ramdas Bagawade1
, Pradeep Patil2
1
Computer Engineering, Vidya Pratishthans College of Engineering, Baramati, India.
2
Information Technology, Vidya Pratishthans College of Engineering, Baramati, India.
ABSTRACT
NOW day’s resolution of image is an important issue in almost all image and video processing
applications like, feature extraction, video resolution enhancement, and satellite image resolution
enhancement. Satellite images are used in various applications like geoscientific studies, astronomy,
and geographical information systems.
In image processing to increase number of pixels in digital image is called as interpolation.
There are different traditional image interpolation techniques such as Bilinear Interpolation, Nearest
Neighbor Interpolation, Bicubic Interpolation and Lanczos Interpolation etc, but compare to all
traditional methods the image resolution enhancement method that use wavelet transform gives better
result. Resolution enhancement techniques which are not based on wavelets get affected by the
drawback of loosing high-frequency components (i.e. edges), which results in blurred output. But
Wavelet transform retains high frequency components. Wavelet transform provides time and
frequency representation simultaneously.
In this work we are using SWT (Stationary Wavelet Transform) and DWT (Discrete Wavelet
Transform) to enhance image resolution and then intermediate subbands of image produced by SWT
and DWT are interpolated by using Lanczos interpolation. Finally we combine all subbands by using
IDWT (Inverse Discrete Wavelet Transform).
Keywords: Discrete Wavelet Transform (DWT), Inverse Discrete Wavelet Transform (IDWT), Peak
signal-to-noise ratio (PSNR), Root mean square error (RMSE), Stationary Wavelet Transform
(SWT).
I. INTRODUCTION
SATELLITE images are utilized in many applications such as geoscientific studies,
astronomy, and geographical information systems. Resolution of an image is always an important
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issue in almost all image and video processing applications, such as video resolution enhancement,
feature extraction and satellite image resolution enhancement.
In image processing to increase number of pixels in digital image is called as interpolation.
Interpolation has been widely used for resolution enhancement. Interpolation has been widely used in
almost all image processing applications such as multiple description coding, facial reconstruction,
and image resolution enhancement. There are four popular interpolation techniques named as nearest
neighbor, bilinear, bicubic and Lanczos [1]. Nearest Neighbor result in significant Jaggy Edge
distortion. The Bilinear Interpolation result in smoother edges but somewhat blurred appearance
overall. Bicubic Interpolation looks best with smooth edges and much less blurring than the bilinear
result [2]. The Lanczos interpolation which is nothing but windowed form of a sinc filter is better
than other traditional interpolation techniques like nearest neighbor, bilinear, and bicubic
interpolation, because of increased ability to detect edges and linear features [1]. Resolution
enhancement techniques which not use wavelets get affected by the drawback of loosing high-
frequency components, which produce blurred output. But Wavelet Transform retains these high
frequency components. Wavelet transform provides time and frequency representation
simultaneously. The high frequency subbands obtained by applying SWT on the original input image
are then interpolated by Lanczos interpolation to get high frequency subbands in order to get correct
estimated coefficients. In this work we are using SWT and DWT to enhance image resolution and the
intermediate subbands of image produced by SWT and DWT are interpolated by using Lanczos
interpolation. Finally we combine all subbands by using IDWT. We can apply this image resolution
enhancement technique in multitemporal image change detection [3], which is nothing but an
application of this image resolution enhancement technique.
First step in multitemporal image change detection is finding the difference image of satellite
image taken at two different time stamps of same geographical area then enhancing same by above
resolution enhancement technique, which produce enhanced difference image. Finally we get change
detection result by applying k-mean algorithm on enhanced difference image only.
II. LITERATURE SURVEY
There are four well-known traditional interpolation techniques namely nearest neighbor,
bilinear, bicubic and Lanczos. In [4] using bilinear, bicubic method the PSNR values for Lena’s
image are 26.34 and 26.86. W. Knox. Carey, Daniel. B. Chuang, and S. S. Hemami in [5] presented
the regularity-preserving interpolation technique for image resolution enhancement synthesizes a new
wavelet subband based on the known wavelet transform coefficients decay. Which gives PSNR (db)
value for Lena’s Image as 31.7 [5]. Xin. Li and Michael. T. Orchard in [6] presented a hybrid
approach produced by combining bilinear interpolation and covariance-based adaptive interpolation
called New Edge-Directed Interpolation Which gives PSNR(db) value for Lena’s Image as 28.81 [4].
Alptekin. Temizel and Theo. Vlachos in [7] presented technique named “Wavelet domain image
resolution enhancement using cycle-spinning and edge modelling ”, which improves PSNR (db)
values for Lena’s image up to 29.27 [4]. Hasan. Demirel and Gholamreza. Anbarjafari in [8]
presented an approach DT- CWT based image resolution enhancement which gives PSNR (db) value
for Lena’s Image as 33.74 [4]. Gholamreza. Anbarjafari and Hasan. Demirel in [9] presented a
method named “Image super resolution based on interpolation of wavelet domain high frequency
subbands and the spatial domain input image”, which gives PSNR(db) value for Lena’s image up to
34.79 [4]. Hasan. Demirel and Gholamreza. Anbarjafari in [4] presented new method named “Image
Resolution Enhancement by Using Discrete and Stationary Wavelet Decomposition”, which give
PSNR(db) value for Lena’s image as 34.82 [4].

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III. PROPOSED METHOD
Input to this technique is the low resolution image of size (m × n). In first step apply SWT and
DWT simultaneously on original image. SWT will create four subband images namely LL, LH, HL
and HH (of same size as that of input image) also DWT will create four subband images namely LL,
LH, HL, and HH (of half size as that of input image). Then in second step apply Lanczos
interpolation with factor 2 on LH, HL and HH subbands produced by DWT. Then in step three add
LH subband of SWT with LH subband of DWT obtained in second step, add HL subband of SWT
with HL subband of DWT obtained in second step and add HH subband of SWT with HH subband of
DWT obtained in second step, which produces Enhanced (Estimated) LH, HL and HH respectively.
Then in step four apply Lanczos interpolation with factor α/2 on original low resolution image, LH,
HL and HH (subbands obtained in step three), give these four images as input to IDWT which
produces high resolution image (αm × αn) which is outcome of our system.
Fig.1 SWT, DWT and Lanczos Interpolation

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A. Discrete Wavelet Transform
Fig.2 DWT
Apply 1-D discrete wavelet transform (DWT) first along the rows of the image, and then along
the columns to produce 2-D decomposition of image [10]. DWT produce four subbands LL (low
low), LH (Low High), HL (High Low) and HH (High High).By using these four subbands we can
regenerate original image by passing the four subbands to IDWT. DWT produce four subbands of
half of original image size while SWT produce four subbands (LL, LH, HL, and HH) of same size as
that of original image.
…. (1)
DWT will be obtained by using formula:
…. (2)
…. (3)

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IDWT will be obtained by using formula:
….. …. ……………. (4)
Equations 1, 2, 3 and 4 are referred from [13].
B. Stationary Wavelet Transform
The Stationary wavelet transform is a wavelet transform algorithm which is created to remove
lack of translation-invariance of discrete wavelet transform (DWT). Translation-invariance is
obtained by removing the upsamplers and downsamplers in DWT and also upsampling in the jth
level, filter coefficients by factor of 2j−1 of DWT algorithm. The SWT is ambiguous scheme as
output of each level of SWT contains same number of samples as that of input, so for decomposition
of N levels there is ambiguity of N in the wavelet coefficients. SWT also known as undecimated
wavelet transform (is as shown in Fig.3) is similar to that of DWT just the size of subbands produced
by SWT is same as that of input image size because it not use downsampling as it is used in DWT.
Fig.3 SWT
C. Lanczos Interpolation
We are using Lanczos interpolation function in two dimensions for this work. We can perform
interpolation of a two dimensional image f by using Lanczos filter of order n by using following
formula [11]:
…. (5)
Where (x, y) is nothing but coordinates of the interpolation point and is maximum value
integer which is less or equal to the parameter value (i.e. floor operator). Flux is preserved by
applying filter weight w as divisor, which can be obtained by following formula [11]:
…. (6)

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Lanczos interpolation makes use of neighborhood of 2n × 2n nearest pixels in mapped square.
As two dimensional Lanczos filter is no separable, so Lanczos interpolation algorithms complexity is
O (N×4 n2) [11].
D. Peak to Signal Noise Ratio
PSNR can be obtained by using following formula [10]:
………. (7)
Where R is the maximum fluctuation in the input image (255 in here as the images are
represented by 8 bit, i.e., 8-bit grayscale representation have been used radiometric resolution is 8
bit). When the two images are identical, the MSE will be zero. For this value the PSNR is undefined
(see Division by zero). MSE is representing the MSE between the given input image Iin and the
original image Iorg which can be obtained by the following formula [10]:
…….. …. (8)
IV. RESULT AND DISCUSSION
This section present the PSNR values of different images obtained by different image
resolution enhancement techniques. The application was coded and compiled in the JAVA 1.6. The
obtained results might slightly differ for image settings. We used various images for testing. From
the obtained results we can conclude that the image resolution enhancement techniques based on
wavelet transform gives good result than other. Max PSNR value means good image quality hence
this approach can also be used for image resolution enhancement.
Fig.4 Satellite Image-II [12], [10]

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Fig.5 Input Images [10], [4]
Table I: Performance Comparison for Satellite Image-I
Technique PSNR (dB)
Bilinear [10] 19.07
Bicubic [10] 20.16
WZP [10] 19.26
WZP-CS [10] 21.09
CWT [8] 24.08
DWT SWT Bicubic [10] 24.97
Our Method 46.657948
Table II: Performance Comparison for Baboon Image
Technique PSNR (dB)
Bilinear [4] 20.51
Bicubic [4] 20.61
WZP [4] 21.47
WZP-CS[4] 21.54
CWT [4] 23.12
Our Method 27.058

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Figure 6 Graph-I (for Satellite Image-I)
Fig.7 Graph-II (for Baboon’s image)
Graph-I is based on PSNR values obtained for satellite image-I using different techniques
while graph-II is based on PSNR values obtained for Baboon’s image. In both graph’s we can see
that PSNR value using proposed method is greater than any other method.
CONCLUSION
Table-I Table-II, Fig.6 and Fig.7 shows that the image resolution enhancement using DWT
and SWT gives better result than other techniques studied in this work. The Lanczos interpolation
which is windowed form of a sinc filter is superior to other traditional interpolation techniques such
as nearest neighbor, bilinear, bicubic Interpolation.
We use DWT, SWT and Lanczos Interpolation method for resolution enhancement. This
approach gives better result in comparison to other method. For Baboon image we get PSNR value
27.0758dB. We conclude that this approach can also be used for image resolution enhancement.

9. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
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REFERENCES
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AUTHOR’S PROFILE
Ramdas Bagawade1
received the B.E. degree in Computer Engineering from
Vidya Pratishtans College of Engineering, Baramati in 2008. He is currently
pursuing M.E. Computer from Pune University.
Pradeep Patil2
has completed B.E. degree in 1995 from Dr. Babasaheb
Ambedkar Marathawada University at Aurangabad. Also completed M.E. Degree in
2005 from Shivaji University Kolhapur. Presently he is working in the Department
of Information Technology at VPCOE Baramati as an Assistant Professor.