G0443640

Aswathy Mohan et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 1), April 2014, pp.36-40
www.ijera.com 36 | P a g e
Image Enhancement Using DWT DCT and SVD
Aswathy Mohan, Mary Linda P A
Mtech, Department of Computer Science, Model Engineering College, Thrikkakara
ABSTRACT: Image enhancement deals with enhancing the image so that it provides more details. Several
techniques are proposed for contrast enhancement of a low-contrast satellite images and CT scans. Here a new
technique has been proposed based on the Discrete Wavelet Transform(DWT) Singular Value Decomposition
(SVD) and Discrete Cosine Transform (DCT). The proposed technique divides image into blocks and converts
each block of image into the DWT-SVD-DCT domain after normalizing the singular value matrix. Then the
modified image is reconstructed by using inverse DCT and DWT and the blocks are combined. Adaptive
Histogram Equalization (AHE) has been used here. Results of the proposed method clearly indicates increased
efficiency and flexibility perceptually and quantitatively over the existing methods like DWT-SVD technique.
Keywords– Adaptive histogram, DCT, DWT, Histogram Equalization, SVD
I. INTRODUCTION
Digital Image processing deals with
processing of digital images. Digital images have
digitized value of intensities. Image enhancement
deals with enhancing images so that visual quality of
image improves thus providing more information.
Medical Imagery deals with images that are used for
medical purposes like from CT scans MRI scans.
Enhancement of such images gives better
understanding of diseases. Here an enhancement
method using DWT DCT and SVD transform is
proposed. This uses advantages of the three
transforms for image enhancement.
II. PROPOSED METHOD
Satellite images are low contrast and dark
images, which has complete information but is not
visible. Similarly CT scans are also dark images . So
the enhancement of such images will help to get more
information. The problem is how the contrast of an
image can be improved from the input satellite
images and CT images. Here a new contrast
enhancement technique is proposed. There are 3 parts
involved. First one is dividing the image into 4
blocks so that the operation can be done on each
block. Then DWT followed by DCT and SVD. The
result shows that images are visibly enhanced using
DWT-DCT-SVD method by incorporating AHE.
2.1 Histogram Manipulation
The histogram of an image is a plot of
number of occurrences of gray levels in the image
against the gray level values. The histogram provides
a convenient summary of the intensities in an image.
Equalisation is the process that attempts to spread
gray level in an image so that they are evenly
distributed across their range. Histogram equalization
reassigns the brightness values of pixels based on
image enhancement. Histogram equalization provides
more visually pleasing results.
Adaptive Histogram Equalization (AHE)
computes several histograms, each corresponding to a
distinct section of the image, and uses them to
redistribute the lightness values of the image. It is
therefore suitable for improving the local contrast of
an image. Adaptive histogram equalization
transforms each pixel with a transformation function
derived from a neighborhood region. It enhances the
contrast of images by transforming the values in the
intensity image using contrast-limited adaptive
histogram equalization (CLAHE). It operates on
small data regions (tiles) and each tile's contrast is
enhanced, so that the histogram of the output region
approximately matches the specified histogram. The
neighboring tiles are then combined using bilinear
interpolation in order to eliminate artificially induced
boundaries. The contrast, especially in homogeneous
areas, can be limited in order to avoid amplifying the
noise which might be present in the image.
2.2 DWT
The decomposition of images into various
frequency ranges permits the isolation of the
frequency into certain sub-bands. This process results
in isolating small changes in an image mainly in low
frequency sub-band images. The 2D wavelet
decomposition of an image is performed by applying
1D DWT along the rows of the image first, and, then,
the results are decomposed along the columns. This
Decomposition results in four decomposed sub-band
images referred to as low-low (LL), low-high (LH),
high-low (HL), and high-high (HH). The Haar
wavelet was introduced in 1910. It is a bipolar step
function. The other wavelets are Daubechies
Wavelet, Morlet Wavelet, Mexican Hat Wavelet and
Shannon Wavelet.
RESEARCH ARTICLE OPEN ACCESS

2.3 DCT
The DCT transforms or converts a signal
from spatial domain into a frequency domain. DCT is
real-valued and provides a better approximation of a
signal with few coefficients. This approach reduces
the size of the normal equations by discarding higher
frequency DCT coefficients. Important structural
information is present in the low frequency DCT
coefficients. Hence, separating the high-frequency
DCT coefficient and applying the illumination
enhancement in the low–frequency DCT coefficient,
it will collect and cover the edge information from
satellite images. The enhanced image is reconstructed
by using inverse DCT and it will be sharper with
good contrast.
2.4 SVD
SVD is based on a theorem from linear
algebra which says that a rectangular matrix A, which
is a product of three matrices that is (i) an orthogonal
matrix UA, (ii) a diagonal matrix ΣA and (iii) the
transpose of an orthogonal matrix VA. The singular-
value-based image equalization (SVE) technique is
based on equalizing the singular value matrix
obtained by singular value decomposition (SVD).
SVD of an image, can be interpreted as a matrix, is
written as follows:
Basic enhancement occurs due to scaling of
singular values of the DCT coefficients. The singular
value matrix represents the intensity information of
input image and any change on the singular values
change the intensity of the input
image.
The main advantage of using SVD for image
equalization, ΣA contains the intensity information of
the image.
2.5 Algorithm
In the proposed technique, initially the input
image „A‟ is processed through AHE to generate
„newA‟ image. Then the DWT of the orginal image
and „newA‟ image is taken. After getting this, the LL
of both of these images are transformed by DCT into
the lower frequency DCT coefficient and higher–
frequency DCT coefficient. Then, the correction
coefficient for the singular value matrix can be
calculated by using:
Where numerator is the lower-frequency
coefficient singular matrix of the DWT of satellite
input image, and denominator is the lower-frequency
coefficient singular matrix of the DWT of satellite
output image of the Adaptive Histogram Equalization
(AHE). The new satellite image (D) is determined by:
---- is the lower DCT frequency component of the
original image that is reconstructed by applying the
inverse operation (IDCT) to produce equalized image
is …………………………
Then the IDWT of newA with LH HL HH
components gives the enhanced image.
The steps is as follows
1. Divide the image into 4 blocks
2. Apply AHE to the image A to get newA
3. Take DWT of the resultant image and
decompose into LL LH HL and HH
[LL, LH, HO, HH] = DWT (newA)
4. Take DCT of LL component
5. Apply DWT to Orginal Image A and decompose
them into LLA LHA HLA HHA
6. Apply DCT to LLA
7. Take SVD of the two DCT applied images and
take correction coefficient for the singular value
8. Obtain new LL image by multiplying U,
correction coefficient, ∑ ,V values from SVD
9. Take IDCT of the LL image to get ̄A
10. Apply IDWT to ̄A image and LHA HLA HHA
11. Combine the 4 blocks of the image to form the
original image
2.6 Performance measures
The performance of this method is measured
in terms of following significant parameters:

Mean (μ) is the average of all intensity
value. It denotes average brightness of the image,
where as standard deviation is the deviation of the
intensity values about mean. It denotes average
contrast of the image. Here I(x, y) is the intensity
value of the pixel (x, y), and (M, N) are the dimension
of the Image.
RESULT
Mean (μ) is the average of all intensity
value. It denotes average brightness of the image,
where as standard deviation is the deviation of the
intensity values about mean. It denotes average
contrast of the image. Here I(x, y) is the intensity
value of the pixel (x, y), and (M, N) are the dimension
of the Image [6]. The results for the enhancement of
satellite images and CT Scans are given in fig 3.1.
The visual and quantitative result shows that the
proposed method has increased efficiency and
flexibility. The resultant images for the enhancement
of satellite images are given below fig 3.3, the
following resultant images of DWT-DCT-SVD gives
the better contrast as well as high image quality.
Fig 3.1 Input CT Scan. Image Courtesy[13]
Fig 3.2 Output CT Scan.
Fig 3.3 Input Satellite Image. Image Courtesy[14]
Fig 3.4 Output Satellite Image
The quality of the visual results indicates
that the proposed technique is sharper and brighter

than existing technique as compared. After obtaining
mean and standard deviation, it is found that the
proposed algorithm gives better results in comparison
with the existing techniques. Mean (μ) represent the
intensity of the image and the standard deviation
represent (σ) the contrast present in the images. The
proposed method represents the better contrast as
well as better brightness with appropriate contrast. In
order to exhibit the superiority of the proposed
methodology two different images have been taken
for analysis. The singular values denote luminance of
each image layer after decomposition using DWT
and DCT methodology. The Mean (μ) & standard
deviation (σ ) values are given below for analysis of
this result. Here we can observe that the proposed
method gives better contrast as well as better
brightness than the DWT SVD method.
Table 3.1: Comparison of the results between
proposed methodology and already existing
technique
Mean Standard Deviation
Input Satellite
Image
179.0545 12.3043
DWT+SVD 157.0131 11.1123
Proposed
Technique
168.5849 29.1964
Input CT Scan
Image
88.2227 88.1706
DWT+SVD 90.5319 90.4389
Proposed
Technique
94.3802 98.2193
From the Table 3.1 above its clear that the mean and
standard deviation of the CT scans have increased
significantly and the output image shows increase in
visibility. For satellite image mean has decreased but
standard deviation has increased.
III. CONCLUSION
In this paper, a new technique has been
proposed based on the Discrete Wavelet Transform
(DWT), Singular Value Decomposition (SVD) and
Discrete Cosine Transform (DCT) that means DWT-
DCT-SVD domain for enhancement of low-contrast
satellite and CT Scan images. As the block
decomposition approach is used each block is
processed separately thus providing more local
enhancement. The basic enhancement occurs due to
scaling of singular values of the DCT coefficients of
the lower Sub-band of DWT. Performance of this
technique has been compared with existing contrast
enhancement techniques DWT-SVD based technique.
From the above experimental results, it can be
concluded that the proposed algorithm is effective in
enhancing low contrast images and the visibility
improvement. The results show that the proposed
technique gives better performance in terms of
contrast (variance) as well as brightness (mean) of
the enhanced. Thus, this technique can be considered
suitable for enhancement of low contrast satellite
image and CT Scans.
In future this work can be extended to color
images as well. Instead of SVD PCA method can be
used for enhancement.
References
[1] R. C. Gonzalez, and R. E. Woods, “Digital
Image Processing”, Englewood Cliffs, NJ:
Prentice-Hall, 2007
[2] G.Praveena, M.Venkatasrinu, A Modified
SVD-DCT Method for Enhancement of Low
Contrast Satellite Images, International
Journal Of Computational Engineering
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[3] Ganesh naga sai Prasad. V , Habibullah
khan , Image enhancement using Wavelet
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[6] Hasan Demirel, Cagri Ozcinar, and
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[8] Hasan Demirel and Gholamreza Anbarjafari,
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PROCESSING, 20( 5)
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[10] Kirk Baker,” Singular Value Decomposition
Tutorial”. March 29, 2005
[11] T. K. Kim, J. K. Paik, and B. S. Kang, Contrast
enhancement system using spatially adaptive
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[13] http://www.intjem.com/content/4/1/64/figure/F
4
[14] http://gal1.piclab.us/key/photos lowcontrast

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