 Open Access
 Total Downloads : 306
 Authors : Miss Smita. A. Patil, Prof. (Dr. ) Mrs. L. S. Admuthe
 Paper ID : IJERTV4IS120457
 Volume & Issue : Volume 04, Issue 12 (December 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS120457
 Published (First Online): 23122015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Image Resolution Enhancement using Discrete, Stationary and Dual Tree Wavelet Transform
Miss. Smita. A. Patil
Assistant Professor, Electronics Dept DKTEs Textile & Engg. Institute Ichalkaranji, India.
Prof. (Dr.) Mrs. L. S. Admuthe

Electronics DKTEs Textile & Engg. Institute
Ichalkaranji, India.
AbstractImage resolution enhancement technique based on interpolation of the high frequency subband images obtained from discrete, stationary and Dual tree Complex wavelet transform(DTCWT).In this study, a comparison of two image resolution enhancement techniques in wavelet domain is done. Each method is analyzed quantitatively and visually. On the basis of analysis, the most efficient method is proposed. The algorithms uses low resolution image as the input image and then wavelet transform is applied to decompose the input image into different high and low frequency subbands. Then these subband images along with the input image are interpolated. Finally all these images are combined to generate a new resolution enhanced image by using inverse process.
Keywords Discrete Wavelet Transform, Stationary Wavelet Transform, Dual Tree Complex Wavelet Transform Interpolation.

INTRODUCTION

Resolution is an important property of an image. Image resolution enhancement is the process of manipulating an image so that resultant image is of good quality image. So to increase the resolution of image there are some few techniques are available. But to increase the resolution of image the best technique is bicubic interpolation with the help of DWT and SWT decomposition [1]. The interpolation technique has been used in many image processing applications such as super resolution [23]. Multiple description coding [4] and facial reconstruction [5].Image resolution enhancement in wavelet domain is relatively a new research topic. Discrete wavelet transform (DWT) [6] is one of the recent wavelet transforms used in image processing. DWT decomposes an input image into different subband images, like lowlow (LL), lowhigh (LH), highlow (HL), and highhigh (HH). Another recent wavelet transform which has been used in different image processing applications is stationary wavelet transform (SWT) [7]. In short, SWT is similar to DWT but it does not use downsampling due to this the subbands will have the same size as the input image.
In this work, two different image resolution enhancement techniques are proposed which gives sharper high resolution image. In first technique DTCWT is applied on input image to decompose input image into different subbands. The high frequency sub bands obtained from DTCWT decomposition are interpolated using bicubic interpolation and these interpolated images are combined by using IDTCWT to get high resolution image. In second technique DWT and SWT is applied on input image to get high frequency subband image. These high frequency sub bands are interpolated using
bicubic interpolation technique and interpolated images are combined by using the inverse DWT to achieve the high resolution image. Both these proposed techniques are compared to get efficient technique
II PROPOSED METHODS

DTCWT technique
To increase the resolution of image, preserving the edges is important. Because image resolution enhancement using interpolation causes loss on its high frequency components, this is caused due to interpolation which smoothens the image hence it is essential to preserve the edges.
In this technique, DTCWT has been employed in order to preserve edges (i.e) highfrequency components of the image. The DTCWT has good directional selectivity as compaired to discrete wavelet transform (DWT).The DT CWT is approximately shift invariant, unlike the critically sampled DWT. The redundancy and shift invariance of the DTCWT means that DTCWT coefficients are inherently interpolable[8].In this method, DTCWT is used to decompose an input image into different low and high frequency subband images. Six complexvalued high frequency subband images contain the highfrequency components of the input image. An interpolation is applied to these highfrequency subband images. In the wavelet domain, the lowresolution image is obtained by lowpass ltering of the highresolution image [9]. i.e, lowfrequency subband images are the low resolution of the original image. Therefore, instead of using lowfrequency subband images, which contain less information, we are using the input image for the interpolation. Hence, using the input image instead of the lowfrequency subband images increases the quality of the high resolution image.The input image is interpolated with the half of the interpolation factor used to interpolate the highfrequency subbands, as illustrated in Fig. 1. By interpolating the input image by /2 and highfrequency subband images by and then following inverse process by using IDTCWT, gives output image which contain sharper edges than the output image obtained by interpolation of the input image directly. In short, the proposed technique interpolates both the input image and the highfrequency subband images obtained through the DTCWT process. The nal highresolution output image is obtained by using the IDTCWT of the interpolated subband images and the input image.
Input image
DTCWT
Interpolation with a factor /2
Low frequency subband images
+75 +45 +15 15 45 75
Iterpolation with factor
+75
+45
High resolution image
IDTCWT
15
45
75
output i.e. LH, HL and HH of DWT technique is interpolated by using the bicubic interpolation technique with enlargement factor of 4. LH, HL and HH of SWT technique is interpolated by using the bicubic interpolation technique with enlargement factor of 2. Now three high frequency components i.e LH, HH, HL of both DWT and SWT technique have the same size hence they are added together to get estimated high frequency subbands. These estimated high frequency subbands are again interpolated by factor /4. Finally output of this bicubic interpolation and the
+15
High frequency subband images Interpolated high frequency subband images
Fig.1. Block diagram of DTCWT
The real 2D dualtree DWT of an image x is implemented using two criticallysampled 2D DWTs in parallel. Then for each pair of subbands sum and difference is calculated. The complex 2D DTDWT also gives wavelets in six distinct directions. The complex 2D dualtree is implemented as four criticallysampled separable 2D DWTs operating in parallel as shown in figure(2).This 2D structure uses four trees for analysis and synthesis. The pair of conjugate filters applied to
original image which is interpolated by factor /2 are combined by using inverse DWT (IDWT) to get the high resolution image. Figure3 shows the block diagram of proposed image resolution enhancement technique. Final high resolution image contains sharper edges than interpolation of input image directly.
Low resolution
Image (m Ã— n)
two dimensional images (x, y) can be expressed as:
SWT
DWT
Tree a(hx, hy)
Tree a(hx, hy)
Analysis Synthesis
LL LH HL HH
LL LH
HL HH
Tree b(hx, hy)
Tree b(hx, hy)
Interpolation with factor 2
Interpolation with factor 2
Interpolation with factor 2
Interpolation with factor 4
Interpolation Interpolation with factor 4 with factor 4
x(t )
Real tree
~x(t)
+ + +
Tree c(hx, hy)
Tree d(hx, hy)
Tree d(hx, hy)
Imaginary tree
Fig. 2: Filter bank structure for 2D DTDWT

ALGORITHM

Input Low Resolution image.

Apply DTCWT on input image.
High resolution image
(m Ã— n)
Interpolation with factor /2
Estimated HH
Estimated HL
Estimated LH
IDWT
Interpolation with factor /4

Apply Bicubic interpolation with factor 4 and 2 to high frequency subband images of DTCWT and input image respectively.

Add interpolated high frequency subbands of SWT and DWT technique to get the estimated subbands.

Apply IDWT to get high resolution image.



DWT SWT technique
This proposed technique uses low resolution image (mÃ—n) then one level DWT is applied to decompose an input image into four different sub bands like LL, LH, HL, and HH. In this technique DWT is used to preserve the high
Fig3.Block diagram of DWTSWT
The decomposition of image after applying one level DWT and SWT are shown in figure 4LowLow (L.L) LowHigh (LH.), HighLow(HL.), HighHigh (HH.) Frequency component.
frequency component of image. The LowHigh (LH), High Low (HL), High High (HH) subband contains high frequency component of input image. Due to down sampling in DWT there is loss of information in subbands hence to minimize this loss SWT is used. The SWT technique
First level Decomposition
Second level Decomposition
Image
LL1 
LH1 
HL1 
HH1 
LL2 
LH2 
LH1 
HL2 
HH2 

HL1 
HH1 
decomposes the input image using haar wavelet into four different sub bands i.e. LL, LH, HL, HH. The high frequency
Fig.4. Structure of Wavelet decomposition
g2 (n)
p(n)
p(n)
g2 (n)
p(n)
g3(n)
I/P image
Fig.5. Structure of SWT decomposition
LPF
Low pass filter 

High pass filter 

2
2
PSNR in DB given as
Where
R= peak value of the input image
M & N are the size of the images, M = no. of rows N= no. of columns and are the matrix element of the reconstructed image and the original image at (i,j)th pixel respectively. The result in table1 shows that proposed method1 is superior than method2.
I/P image
HPF
Table1 .Observation Table
PSNR(dB) 

Method/Image 
Proposed Method1 
Proposed Method2 
Lena 
29.89 
39.64 
Elaine 
28.61 
41.67 
Baboon 
28.69 
47.67 
Pepper 
29.10 
41.96 
2
LPF 

HPF 

2 2
2
FIG.6. STRUCTURE OF DWT DECOMPOSITION
The figure 5 and 6 shows the structure of SWT and DWT detail coefficient and approximation coefficient of image LowLow(L.L) LowHigh(L.H.), HighLow(H.L.), High High(H.H.) frequency component.

ALGORITHM

Input Low Resolution image.

Apply DWT and SWT on input image.

Apply Bicubic interpolation with factor 4 and 2 to three high frequency subband images of DWT and SWT respectively.

Add interpolated high frequency subbands of SWT and

RESULTS AND DISCUSSION
Figure7 and Figure 8 shows the low resolution input & high resolution output Lena image of method1& method2 respectively. Table 1 compares the PSNR performance of both DTCWT & DWT, SWT technique. The result in table1 indicates that the DWT, SWT technique gives much better result as compared DTCWT technique.Table1 shows that PSNR value is increased by 10dB using DWT, SWT technique than DTCWT.
DWT technique to get the estimated subbands.


Interpolate estimated subbands by factor /4.

Apply IDWT to the interpolated HF subbands and LL band of SWT image to get high resolution image.


PERFORMANCE PARAMETER
Here Peak Signal to Noise Ratio (PSNR) is calculated to analyze quality of image.Table1 compares PSNR results of two proposed technique. Different types of images such as Lena, Elaine, Baboon, Peppers are tested by this algorithm. The PSNR calculation of two images, one original and reconstructed image, describes how far two images are equal.
Original Image 128 x 128
High Resolution Image 512 x 512
Fig.7. method1 images
Original Image 128 x 128
High Resolution Image 512 x 512
Fig.8. method2 images

CONCLUSION
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