International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Image Resolution Enhancement Technique Based on
the Interpolation of the High Frequency Subbands
Obtained by DWT
Mrs.S.Sangeetha#1, Mr.Y. Hari Krishna*2,
#
M.Tech Student, ECE Dept., BIT Institute of Technology, Hindupur.
Anantapur (Dist), Andhra Pradesh, India.
Abstract— In this correspondence, the authors propose an
image resolution enhancement technique based on interpolation
of the high frequency sub band images obtained by discrete
wavelet transform (DWT) and the input image. The edges are
enhanced by introducing an intermediate stage by using
stationary wavelet transform (SWT). DWT is applied in order to
decompose an input image into different sub bands. Then the
high frequency sub bands as well as the input image are
interpolated.
The estimated high frequency sub bands are being modified
by using high frequency sub band obtained through SWT. Then
all these sub bands are combined to generate a new high
resolution image by using inverse DWT (IDWT). The
quantitative and visual results are showing the superiority of the
proposed technique over the conventional and state-of-art image
resolution enhancement techniques.
The main aim of this image resolution enhancement is to
produce a high resolution image with high PSNR from a low
resolution image. If we adopt this method of resolution
enhancement this helps in viewing even a low resolution image
with high clarity i.e in case of seeing satellite images.
Keywords— DWT, SWT, PSNR, IDWT, WZP, Interpolation.
I. INTRODUCTION
DWT decomposes an image into different subband
images, namely low-low (LL), low-high (LH),
high-low (HL), and high-high (HH). Another recent
wavelet transform which has been used in several
image processing applications is stationary wavelet
transform (SWT). In short, SWT is similar to DWT
but it does not use down-sampling, hence the
subbands will have the same size as the input image.
In this work, we are proposing an image
resolution enhancement technique which generates
sharper high resolution image. The pro-posed
technique uses DWT to decompose a low resolution
image into different subbands. Then the three high
frequency subband images have been interpolated
using bicubic interpolation [5], [6]. The high
frequency sub-bands obtained by SWT of the input
image are being incremented into the interpolated
high frequency subbands in order to correct the
estimated coefficients.
Resolution has been frequently referred as an
important aspect of an image. Images are being
processed in order to obtain more enhanced
resolution. One of the commonly used techniques
for image resolution enhancement is Interpolation.
Interpolation has been widely used in many image
processing
applications
such
as
facial
reconstruction, multiple description coding, and
super resolution. There are three well known
interpolation techniques, namely nearest neighbor
interpolation, bilinear interpolation, and bicubic
interpolation.
In parallel, the input image is also interpolated
separately. Finally, corrected interpolated high
frequency Subbands [4] and interpolated input
image are combined by using inverse DWT (IDWT)
to achieve a high resolution output image. The
proposed technique has been compared with
conventional and state-of-art image resolution
enhancement techniques. In this technique input
image is interpolated beforehand, because it is seen
that when a resolution comparison of input image
alone with interpolated input image is done, the
resolution seems to be more for interpolated image
Image resolution enhancement in the wavelet than original image so input image is interpolated
domain is a relatively new research topic and by bicubic interpolation [5], [6].
The conventional techniques used are the
recently many new algorithms have been proposed.
following:
Discrete wavelet transform (DWT) is one of the
recent wavelet transforms used in image processing.
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i)
interpolation
techniques:
bilinear second form of zero padding. It is also used in
interpolation and bicubic interpolation;
conjunction with zero-phase FFT window.
ii) Wavelet zero padding (WZP).
According to the quantitative and qualitative
experimental results, the proposed technique over
performs
the
aforementioned
conventional
techniques for image resolution enhancement.
II. WZP & INTERPOLATION
A Wavelet zero padding
It is one of the simplest methods for image
resolution enhancement. It assumes that the signal
is zero outside the original support. The most
common form of zero padding is to append a string
of zero-valued samples to the end of sometimedomain sequence
Zero padding is used in spectral analysis with
transforms to improve the accuracy of the reported
amplitudes, not to increase frequency resolution.
Without zero- padding, input frequencies will be
attenuated in the output. Zero padding in the time
domain is equivalent to optimal interpolation in the
frequency domain, which restores the correct
amplitudes. Since the wavelet transform is defined
for infinite length signals, finite length signals are
extended before they can be transformed. One of
the common extension methods is zero padding.
Zero padding shifts the intersample spacing in
frequency of the array that represents the result.
Zero padding consists of extending a signal (or
spectrum) with zeros. It maps a length N signal to a
length M>N signal, but need not divide M.
ZeroPad M, m(x) =
x (m), 0≤m≤N-1
0, N≤m≤M-1
For example,
ZeroPad10([1,2,3,4,5])=[1,2,3,4,5,0,0,0,0,0]
The above definition is natural when
x(n) represents a signal starting at time 0 and
extending for N samples. If, on the other hand, we
are zero-padding a spectrum, or we have a timedomain signal which has nonzero samples for
negative time indices, then the zero padding is
normally
inserted
between
samples
(N1)/2 and (N+1)/2 for N odd and similarly for N
even that is for spectra, zero padding is inserted at
the point Z=-1(w=πf0). Below figure illustrates the
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Fig: 1 Illustration of frequency domain zero padding
fig a Original spectrum x=[3,2,1,1,2] plotted over the
domain k є (0,N-1) where N=5
fig b Zeropad11(X)
fig c The same signal interpolated over the domain k є [(N-1)/2,(N-1)/2] which is more natural for
interpreting negative frequencies
fig d Zeropad11(X) plotted over the zero centered domains.
In image resolution enhancement, wavelet
transform of a low resolution (LR) image is taken
and zero matrices are embedded into the
transformed image, by discarding high frequency
sub bands through the inverse wavelet transform
and thus high resolution (HR) image is obtained.
Input
Image (LR)
Wavelet
Transform
WZP
Output
Image (HR)
Inverse Wavelet
Transform
Fig 2 Wavelet zero padding
1) Drawback
i) The discontinuities are artificially created at the
border.
ii) The shift can cause problems if it alters the array
positions relative to the frequency of interest.
B Interpolation
Interpolation is the process of using known data
to estimate values at unknown locations.
Interpolation method select new pixel from
surrounding pixels. Mainly there are two types of
interpolation algorithms
1) Adaptive algorithms
i) This algorithm changes depending on what they are
interpolating.
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ii) It involves lot of calculations
2) Non adaptive algorithms
i) This algorithm interpolate by fixed pattern for all
pixels.
ii) It has the advantage of easy performance and low
calculation cost.
Non adaptive algorithm includes linear interpolation
algorithms. Linear interpolation includes nearest neighbour,
bilinear, Bicubic interpolation. In our project linear
interpolation is used because of drawbacks in adaptive
algorithm.
C Nearest neighbor interpolation
Fig: 3(a) Normal image Fig:3(b) jaggy edge distorted image
E Bicubic interpolation
It goes one step beyond bilinear by considering
the closest 4x4 neighborhood of known pixels —
for a total of 16 pixels. When these are at various
distances from the unknown pixel, closer pixels are
given a higher weighting in the calculation. Bicubic
produces noticeably sharper images than the
previous two methods, and is perhaps the ideal
combination of processing time and output quality.
For this reason it is a standard in many image
editing programs (including Adobe Photoshop),
printer drivers and in-camera interpolation.
Suppose
the
function
values f and
the
derivatives fx, fy and fxy are known at the four
corners(0,0),(1,0),(0,1) and (1,1) of the unit square.
The interpolated surface can then be written as
It is the most basic interpolation technique and
requires the least processing time of all the
interpolation algorithms because it only considers
one pixel — the closest one to the interpolated point.
This has the effect of simply making each pixel
bigger. Nearest neighbour interpolation is a simple
method of multivibrate interpolation in one or two
dimensions.
The nearest neighbour algorithm selects the value
The interpolation problem consists of determining the 16
of the nearest point and does not consider the values coefficients aij.
of neighbouring points at all, yielding a piecewiseconstant interpolant. The algorithm is very simple
to implement and is commonly used in real-time 3D
rendering to
select
colour
values
for
a textured surface.
1) Drawback
It results in jagged edge distortion, where some
information at the edges is lost. It can be seen in
next page.
D Bilinear interpolation
It considers the closest 2x2 neighborhood of
known pixel values surrounding the unknown pixel.
It then takes a weighted average of these 4 pixels to
arrive at its final interpolated value. This results in
much smoother looking images than nearest
neighbor. When all known pixel distances are equal,
then the interpolated value is simply their sum
divided by four.
1) Drawback:
It results in more blurred images.
Fig: 4 Bicubic interpolation on the square [0,3]x[0,3] consisting of 9 unit
squares patched together.
Bicubic interpolation is done as per MATLAB’s
implementation. Colour indicates function value.
The black dots are the locations of the prescribed
data being interpolated and the color samples are
not radially symmetric.
As the more adjacent pixels it includes, the more
accurate it can become. Hence in this project
interpolation is done by bicubic interpolation. But
this comes at the expense of much longer
processing time. But images obtained by these
linear interpolation technique produces many
artifacts like blurring, blocking etc. Hence we do
not depend on interpolation on a whole for image
resolution enhancement. Along with it Discrete and
stationary wavelet transform is used.
1) Advantages
i) Bicubic interpolation creates smoother curves than
bilinear interpolation, and introduces fewer
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"artifacts," or pixels that stand out as conspicuously
deteriorating the apparent quality of the image.
ii) When you need to increase the size of an image and
time isn't important for example, if you're making
prints from a digital camera on your own time
bicubic interpolation provides the smooth results
that are perceived as being of a higher quality.
III. DWT & SWT
A Discrete Wavelet Transform
DWT [3] represents an arbitrary square integrable
function as superposition of a family of basis
functions called wavelets. A family of wavelet basis
functions can be generated by translating and
dilating the mother wavelet corresponding to the
family. The DWT coefficients can be obtained by
taking the inner product between the input signal
and the wavelet functions. Since, the basis functions
are translated and dilated versions of each other, a
simpler algorithm, and known as Mallat’s tree
algorithm or pyramid algorithm.
In this algorithm, the DWT coefficients of one
stage can be calculated from the DWT coefficients
of the previous stage, which is expressed as follows:
the mother wavelet. It is observed from Eq. 2 that j
-th level DWT coefficients can be obtained from (j
+1) -th level DWT coefficients. Compactly
supported wavelets are generally used in various
applications.
In the first level of decomposition, one low pass
sub image (LL2) and three orientation selective
high pass sub images (LH2, HL2, and HH2) are
created. DWT decomposes an image into a pyramid
structure of sub images with various resolutions
corresponding to the different scales.
The inverse wavelet transform is calculated in the
reverse manner, i.e., starting from the lowest
resolution sub images, the higher resolution images
are calculated recursively. We note that no
separable wavelets have also been proposed in the
literature.
However, they are not widely used because of
their complexity.
LL
LH
HL
HH
Fig 5. Wavelet transforms decomposition of an image into 4 sub-images.
Few applications of DWT are:
i) Data compression,
ii) ECG analysis,
iii) Climatology,
iv) Blood pressure etc.
The below figure shows the 2D DWT
Where W L (p, q) is p -th scaling coefficient at
the q –th stage, W H (p, q ) is the p-th wavelet
coefficient at q–th stage, h (n ) and g (n ) are the
dilation coefficients corresponding to the scaling
and wavelet functions, respectively. For computing
the DWT coefficients of the discrete-time data, it is
assumed that the input data represents the DWT
coefficients of a high resolution stage. Eq. 1 can
then be used for obtaining DWT coefficients of
subsequent stages.
In order to reconstruct the original data, the DWT Where
coefficients are up sampled and passed through
another set of low pass and high pass filters, which
are expressed as:
Fig. 6 2D - Discrete Wavelet Transform.
2
1
Downsample Columns
1
2
Downsample Rows
X
Convolve with filter X the rows of the entry
X
Convolve with filter X the rows of the entry
Where h’ (n) and g’ (n) are respectively the low
pass and high pass synthesis filter corresponding to B Stationary Wavelet Transform
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DWT has been employed in order to preserve the
high frequency components of the image. The
redundancy and shift invariance of the DWT mean
that DWT coefficients are inherently interpolable.
In this correspondence, one level DWT is used to
decompose an input image into different subband
images. Three high frequency subbands (LH, HL,
and HH) contain the high frequency components of
the input image. In the proposed technique, bicubic
interpolation with enlargement factor of 2 is applied
to high frequency subband images. Downsampling
[2] in each of the DWT subbands causes
information loss in the respective subbands. That is
Few applications of SWT are:
why SWT is employed to minimize this loss.
i) Pattern recognition
The interpolated high frequency Subbands [4]
ii) Signal denoising
and the SWT high frequency subbands have the
same size which means they can be added with each
other. The new corrected high frequency subbands
can be interpolated further for higher enlargement.
Using input image instead of low frequency
subband increases the quality of the super resolved
image. Below figure illustrates the block diagram of
the proposed image resolution enhancement
technique. By interpolating input image by α/2, and
Fig.7. A 3 level SWT Filter Bank
high frequency subbands by 2 and α in the
intermediate and final interpolation stages
respectively, and then by applying IDWT, the
output image will contain sharper edges than the
interpolated image obtained by interpolation of the
Fig.8. SWT Filters
input image directly. This is due to the fact that, the
interpolation of isolated high frequency components
IV. PROPOSED METHOD
in high frequency subbands and using the
In image resolution enhancement by using corrections obtained by adding high frequency
interpolation the main loss is on its high frequency subbands of SWT of the input image, will preserve
components (i.e., edges), which is due to the more high frequency components after the
smoothing caused by interpolation. In order to interpolation than interpolating input image directly.
increase the quality of the super resolved image,
preserving the edges is essential. In this work,
The Stationary wavelet transform (SWT) is a
wavelet transform algorithm designed to overcome
the lack of translation-invariance of the discrete
wavelet transform (DWT). Translation-invariance is
achieved by removing the downsamplers and
upsamplers in the DWT and upsampling the filter
coefficients by a factor of 2j-1in the jth level of the
algorithm. The SWT is an inherently redundant
scheme as the output of each level of SWT contains
the same number of samples as the input – so for a
decomposition of N levels there is a redundancy of
N in the wavelet coefficients.
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Low Resolution
Image
SWT
LL
LH
HL
DWT
LL
HH
LH
HL
HH
Interpolation with factor 2
+
Estimated
LH
+
Estimated
HL
+
Estimated
HH
IDWT
Interpolation with factor Α/2
Interpolation with factor Α/2
High Resolution
Image
Fig: 9 Block diagram for proposed super resolution algorithm
V. RESULTS AND DISCUSSION
The super resolved image of lena’s picture using
proposed technique in (fig d) is much better than
the low resolution image in (fig a), super resolved
image by using the interpolation (fig b), and WZP
(fig c).
(c)
(d)
Fig. 10. (a) Original low resolution Baboon’s image. (b) Bicubic interpolated
image. (c) Super resolved image using WZP. (d) Proposed technique.
Table 1 compares the PSNR performance of the
proposed technique using bicubic interpolation with
other resolution enhancement techniques: bicubic
interpolation, WZP. In this project resolution of an
image is measured in terms of PSNR.
(a)
(b)
A PSNR
PSNR values are used to measure the quality of
an image. Peak signal-to-noise ratios (PSNR) have
been implemented in order to obtain some
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quantitative results for comparison. PSNR is
usually expressed in terms of logarithmic decibel
value. A higher PSNR generally indicates that the
reconstruction is of higher quality.
TABLE 1
COMPARISON OF RESULTS
Techniques used
Lena (PSNR value)
Bicubic interpolation
Super resolved image
using WZP
Proposed technique
(DWT & SWT)
26.867
29.27
We sincerely thank Mr. Sudarshan Raju, HOD
ECE, BIT IT, Mr. Y. Hari Krishna, Asst. Professor,
BIT IT, Mrs. C. Geetha, Associate Professor, Mrs.
D. Manjula, Asst. Professor, MTIET, Palamaner,
Chittoor, Principal MTIET, Management MTIET,
Palamaner and the Staff members of ECE Dept.
MTIET, family members, and friends, one and all
who helped us to make this paper successful.
REFERENCES
[1]
35.82
[2]
The results in Table I indicate that the proposed
technique over performs the aforementioned conventional
techniques.
[3]
VI. CONCLUSION
This work proposed an image resolution
enhancement technique based on the interpolation
of the high frequency subbands obtained by DWT,
correcting the high frequency subband estimation
by using SWT high frequency subbands, and the
input image. The proposed technique uses DWT to
decompose an image into different subbands, and
then the high frequency subband images have been
interpolated.
The interpolated high frequency subband
coefficients have been corrected by using the high
frequency subbands achieved by SWT of the input
image. An original image is interpolated with half
of the interpolation factor used for interpolation the
high frequency subbands. Afterwards all these
images have been combined using IDWT to
generate a super resolved imaged. The proposed
technique has been tested on well-known
benchmark images, where their PSNR and visual
results show the superiority of proposed technique
over the other resolution enhancement techniques.
The high resolution image thus obtained is used
in
i)
remote sensing
ii) medicine
iii) military information acquisition
iv) multimedia
v) Satellite images etc.
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H. Demirel, G. Anbarjafari, and S. Izadpanahi, “Improved motionbased localized super resolution technique using discrete wavelet
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www.google.com.
ABOUT AUTHORS
1. Mrs.S.Sangeetha received B.Tech
degree from SVCET in 2009, Chittoor
Dist, A.P, and India. She worked as
Asst. Professor in Mother Theresa
Institute of Engineering & Technology
during 2009-11. She has 2 years’
experience in teaching field. Her
Interested areas are Communications,
Digital Image Processing, and VLSI.
2. Mr.Y. Hari Krishna is working as an
Asst. Professor in Dept. of ECE, BIT IT,
Anantapur (Dist), Hindupur, India. He did
his B.Tech in BVCITS , Amalapuram and
M.Tech in SKTRMCE, Mahaboobnagar
(Dist), Kondair. He has 3 years’
experience in teaching field. His
interested areas are DIP, Wireless
Communications etc... He thought several
subjects for under graduate students.
ACKNOWLEDGMENT
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