International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 3 – March 2015
Deblurring and Super Resolution by Sparse
represented Nonlocally Centralized images
B.Chithara#1,NikilSatish*2
#1
PG Scholor, Dept of Electronics and Communication Engineering, Adhiyamaan College of Engineering,
Hosur,Tamilnadu,India
#2
Asst.Professor,Dept of Electronics and Communication Engineering, Adhiyamaan College of
Engineering, Hosur,Tamilnadu,India
Abstract - In image restoration application sparse
representation has been successfully used as powerful
statistical image modeling technique. This results in the
development of l1-norm optimization techniques, and leads
to implement it in some domain.The performance of sparse
representation is improved by introducing sparse coding
noise and thus main objective is to suppress the noise to
show promising results. To obtain good estimates of the
sparse coding coefficients of the original image, nonlocal
self-similar patches are chosen,then it is centralized. This
adaptive method for image restoration is applied to our
extensive experiments to remove blurring and down
sampled images.
Key words-Sparse representation,
Nonlocally centralized,
Self similarity, PSNR, FSIM.
PCA
dictionary,
I. INTRODUCTION
The problem of image restoration (IR) is solved
by reconstructing the image [1],[2],[3] by,
y = Dx+ v
(1)
where generallyDis a degradation matrix, x is the
original image vector and vis the additive noise
vector. But for deblurring the image D is
considered as blurring operator, and for super
resulted image D is considered as composite
operator.There are many algorithms were
existing to compare the PSNR index for degraded
images namely IDD-BM3Ddeblurring method
and the adaptive sparse domain selection
method(ASDS-Reg).The drawback of all other
algorithms is tend to oversmooth and sharpen the
edges due to the assumption of piecewise
constant.
II. PROPOSED SYSTEM
Large
sparse
matricesoften
appear
in scientific or engineering applications.
when
solving partial differential equations. Operations using
standard dense-matrix structures and algorithms are
slow and inefficient when applied to large sparse
matrices as processingand memory are wasted on the
zeroes.
Sparse
data
is
by
nature
more
easily compressed and thus require significantly
less storage. Some very large sparse matrices are
infeasible to manipulate using standard dense-matrix
algorithms. Image restoration is generally known as
reconstructing original image from corrupted image.
This corrupted image may be either noise, blurring nor
down sampled pixels.
ISSN: 2231-5381
In this algorithm,the given image patches are
clustered and each patch of xof original image is
learnt for its PCA sub-dictionary_k.The
distances is calculated for the mean of clusters
and then select the PCA sub-dictionary of this
cluster to code it.The coding coefficients of
sparse
are
selected
using
dictionary
vectors.Bycomparison
of
over-complete
dictionary the values of coefficients are
suppressed.This avoid oversmooth of the images.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 3 – March 2015
III. ALGORITHM OF NCSR
A. PCA Dictionary
The selection of dictionary is an important issues of
sparsity based IR. Principal component analysis (PCA)
involves in learning of sub-dictionaries from given
image itself instead of example image. It is achieved by
orthogonal transformation. The correlated variables are
converted into linearly uncorrelated variables. It reduces
the dimension of given data. Here the data refers to large
number of variables. At first imagex patches are
extracted, then patches are divided into K clusters.PCA
sub-dictionary is used to learn each cluster and code it.
To code each patch we choose one sub-dictionary from
trained K PCA sub-dictionary to code it. It results in a
very good representation of sparse for a given patch.
B. Estimation ofNonlocal sparse code
Sparse code is represented as fraction of zero elements
in the matrix. The codes which are occurring and
growing at widely spaced intervals are taken in account.
Dictionaries of vectors are compared to represent the
code in sparse. This required only few co-efficients to
represent the images. Compression is not required and
bandwidth is also less. In a patch of an image, it
compares the pixels with other and computes average
weight. Average of all patches which are similar are
related. Basically natural images contain repetitive
structures.Due to the presence of rich amount of
nonlocal redundancies, a good estimates of α and β can
be calculated by average weight of sparse code related
with similar patches.Then β can be computed asweighed
average of α.Thus the expression is given as,
For a given patch, algorithm is given by,
1. Initialization:
(a) Set the initial estimate as xˆ = y for
image debluringand xˆ by bicubic
interpolator
for
image
superresolution;
(b) Set initial regularization parameters,
2.Outer loop (dictionary learning & clustering):
iterate on l = 1, 2, . . . ,L
(a)Update the dictionaries {ɸ k } via k-means
&PCA;
(b)Inner loop (clustering): iterate on j = 1, 2, ., J.
(c) compute v(j) ,
(d) compute
(e) update the parameters,
3.display the image,
4.END
β = ∑qɛ Ωi wi,q αi,q (2)
wherewi,q is the weight. The estimation of α and β is
used to improve the accuracy of sparse codes which
results in improvement of IR. The l-norm exceeds from
zero to infinity. The size and the length of all vectors in
a vector space are measured. This procedure is iterated
until convergence. At lthiteration sparse vector is
obtained by solving theminimization problem.
Figure.1 Flowchart of NCSR
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International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 3 – March 2015
IV. DEBLURRING
Deblurring ofimage is applied to both the simulated blurred
images and real motion blurred images. The simulated
image of 9× 9 uniform blur and 2D Gaussian function
with standard deviation 1.6 is considered. The problem
of NCSR algorithm is solved by iterative shrinkage
algorithm[13].It is formulated as
Fig.2Star fish
(
(j)) +
(j)
(3)
PSNR is used to analyze the quality of image, moving
objects in db. PSNR measures values from 0 to 255
pixels. The width and height of the image is considered
along with the mean square error to calculate the PSNR
values. FSIM is measured by choosing features having
similarities.
TABLE 2
Comparsion of FSIM & PSNR for Deblurring
Star fish
PSNR
FSIM
9x9 uniform
blur
σ=1.6
30.28
0.9293
32.27
0.9551
V. SUPER RESOLUTION
In the given down sampled image, for super-resolution
HR image is blurred and LR image is generated.The
experiments is done for various standard deviation and
better result is obtained for 1.6, and then the blurred
image is downsampled by a scaling factor 3 in both
horizontal and vertical directions. The average weight of
the horizontal and vertical directed image is given as
=
(4)
Gaussian blur
σ=1.6
B. Super resolution
In fig 3, from left to right, first image is original
image, second is LR image, and third is
reconstructed image of parrot.NCSR approach
reconstructs better and pleasant HR images.
The additive Gaussian noise for 7x7 Gaussian image
with standarddeviation 5 is also added to the LR images.
Because human visual system is more sensitive to
luminance changes.
VI.RESULT AND DISCUSSIONS
A.Deblurring
In fig 2, from left to right first image denotes blurred
image, second image denotes patches chosen for IDDBM3D approach, third image for ASDS-Reg. Finally the
fourth image with clear view of patches chosen proves
the NCSR approach.
ISSN: 2231-5381
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Fig 2.Parrot
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International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 3 – March 2015
TABLE 2
Comparison of PSNR & FSIM for Super resolution
Parrot
PSNR
FSIM
Scaling factor=3,
σ=5,(ASDS Reg)
29.01
0.9182
Scaling factor=3,
σ=5,(NCSR)
29.51
0.9210
[9] I. Daubechies, M. Defriese, and C. DeMol, “An iterative
thresholding algorithm for linear inverse problems with
a sparsity constraint,” Com-mun. Pure Appl. Math., vol.
57, no. 11, pp. 1413–1457, 2004
[10] M. Zibulevsky and M. Elad, “l1-l2 optimization in
signal and image processing,” IEEE Signal Process.
Mag., vol. 27, no. 3, pp. 76–88, May 2010.
[11] J. A. Tropp and S. J. Wright, “Computational methods
for sparse solution of linear inverse problems,” Proc.
IEEE, vol. 98, no. 6, pp. 948–958, Jun. 2010.
[12] J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new
TwIST: Two-step iterative shrinkage/thresholding
algorithms for image restoration,” IEEETrans. Image
Process., vol. 16, no. 12, pp. 2992–3004, Dec. 2007.
VII. CONCLUSION
In this paper, images are represented in sparse is
considered and the sparse coding noise has been
suppressed in order to get better results. The NCSR
minimization problem has beenefficiently solved
by iterative shrinkage function. This has further
solved thel1-regularizer.Experimental results on
imagedeblurring
and
super-resolution
are
demonstrated using NCSRalgorithm. This shows
the NCSR approach can achieve highly competitive
performance to other leading methods.
ACKNOWLEGEMENT
I hereby like to thank my guide Asst.Prof.NIKIL
SATISH and our head of the department Dr.SUMATHI
for providing me support and all facilities.
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