An Approach for Image Deblurring: Based on Sparse Representation and Regularized Filter

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 431
AN APPROACH FOR IMAGE DEBLURRING: BASED ON SPARSE
REPRESENTATION AND REGULARIZED FILTER
Ragulganthi M*1, Deepa P2, Gayathri G3, Vinoth R4
1Pg scholar, Dept of ECE, Government College of Technology, Coimbatore, Tamilnadu, India
2Assistant professor, Dept of ECE, Government College of Technology, Coimbatore, Tamilnadu, India
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Abstract - Deblurring of the image is most the
fundamental problem in image restoration. The existing
methods utilize prior statistics learned from a set of
additional images for deblurring. To overcome this issue, an
approach for deblurring of an image based on the sparse
representation and regularized filter has been proposed.
The input image is split into image patches and processed
one by one. For each image patch, the sparse coefficient has
been estimated and the dictionaries were learned. The
estimation and learning were repeated for all patches and
finally merge the patches. The merged patches are
subtracted from blurred input image the deblur kernel to be
obtained. The deblur kernel then applied to regularized
filter algorithm the original image to be recovered without
blurring. The proposed deblur algorithm has been
simulated using MATLAB R2013a (8.1.0.604). The metrics
and visual analysis shows that the proposed approach gives
better performance compared to existing methods.
Key Words: Image deblurring, Dictionary learning
based image sparse representation, Regularized
filter
1.INTRODUCTION
Image deblurring is one of the problems in image
restoration. The image blurring causes due to camera
shake. The image blur can be modelled by a latent image
convolving with a kernel K.
B = K ⊗I + n, (1)
Where B, n and I represent the input blurred image,
latent image and noise respectively. The ⊗ denotes
convolution operator and the deblurring problem in
image are thus posed as deconvolution problem [13].
The process of removing blurring artifacts from images
caused by motion blur is called deblurring. The blur is
typically modeled as the convolution of a point spread
function with a latent input image, where both the latent
input image and the point spread function are unknown.
Image deblurring has received a lot of attention in
computer vision community. Deblurring is the
combination of two sub-problems: Point spread function
(PSF) estimation and non-blind image deconvolution.
These problems are both independently in computer
graphics, computer vision, and image processing [13].
Finding a sparse representation of input data in the form
of a linear combination of basic elements. It is called
sparse dictionary learning and this is learning method.
These elements are composing a dictionary. Atoms in the
dictionary are not required to be orthogonal [10]. One of
the key principles of dictionary learning is that the
dictionary has to be inferred from the input data. The
sparse dictionary learning method has been stimulated
by the signal processing to represent the input data using
as few possible components.
To unblurred an image the non-blind deconvolution blur
Point Spread Function (PSF) has been used [14].The
previous works to restore an image based on Richardson-
Lucy or Weiner ﬁltering have more noise sensitivity[15
16]. Total Variation regularizer heavy-tailed normal
image priors and Hyper-Laplacian priors were also
widely studied [17].Blind deconvolution can be
performing iteratively, whereby each iteration improves
the estimation of the PSF [8].
In [3] found that a new iterative optimization to solve the
kernel estimation of images. To deblur images with very
large blur kernels is very difficult. to reduce this difficulty
using the iterative methods to deblur the image. From [1]
found that to solve the kernel estimation and large scale
optimization is used unnaturall0 sparse representation
[1].The properties for latent text image and the difficulty
of applying the properties to text image de-blurring is
discussed in [2].Two motion blurred images with
different blur directions and its restoration quality is
superior than when using only a single image [5].A
deblurring methods can be modelled as the observed
blurry image as the convolution of a latent image with a
blur kernel[6].

The camera moves primarily forward or backward
caused by a special type of motion blur it is very difficult
to handle. To solve this type of blur is distinctive practical
importance. A solution to solve using depth
variation[8].The feature-sign search for solving the l1-
least squares problem to learn coefficients of problem
optimization [9][10] and a Lagrange dual method for
thel2-constrained least squares problem to learn the
bases for any sparsity penalty function.
2. IMAGE DEBLURRING WITH DICTIONARY
LEARNING
To estimate the deblur kernel, an iterative method to
alternately estimate the unknown variables, one at a
time, which divides the optimization problem into
several simple ones in each iteration. Were performed
more importantly, the dictionary D is learned from the
input image during this optimization process. The
algorithm iteratively optimizes one of K, D, α by ﬁxing the
other two, and ﬁnally obtains the deblurring kernel. With
the estimated kernel, any standard deconvolution
algorithm to recover the latent image can be applied. The
initial dictionary and the initial kernel value is
convoluted and this result will be called as dictionary and
this dictionary is subtracted by blur image.
Fig.1 Block diagaram for deblurring algorithm
2.1 Estimate Sparse Coefficient
To follow the below algorithm to estimating the sparse
coefficients of the given input blurred image.
ALGORITHM I
• Step 1: Get the blurred input image B
• Step 2: Spilt the B into four patches as
p1,p2,p3,p4.
• Step 3: Consider first image patch p1 and find the
sparse coefficient to fix K using Gaussian kernel
and D as identity matrix.
α(n+1) = argmin||α||1 (2)
s.t. b =(K(n) ⊗D(n))α (3)
• Step 4: For each iteration the α value should be
updated into D
• Step 5: Take N iterations to estimating the α(n+1).
• Step 6: Repeat the above 5 steps to all image
patches and estimate the α(n+1).
2.2 Updating Dictionary
In the knowledge of previous algorithm using the
sprase coefficient to updating the dictionary of the
image.
ALGORITHM II
• Step 1: To update the dictionary, deconvolve blurred
image with kernel up to Last iteration using any
deconvolution algorithm and get Ip.
• Step 2: Ip image is split into four patches.
• Step 3: Update the dictionary using α(n+1) and D.
D(n+1) = min||Ip −D(n)α(n+1)||2
2. (4)
• Step 4: Repeat the steps 1 to 3 to all image patches
and estimating the D(n+1).
2.3 Recovering Deblur Image
Consider previous algorithm to estimate the deblur
kernel of the image and finally to recovered the deblur
image.
ALGORITHM III
• Step 1: Find the latent image patch using
Ip(n+1) = D(n+1)α(n+1) (5)
• Step 2: Merge the all image patches of Ip.
• Step 3: The reconstructed image is subtracted from
the blurred input image to obtain the deblur kernel.
•Step 4: Perform the deconvolution with the input
blurred image and Deblur kernel using wiener
deconvolution method.
•Step 5: Apply the regularization filter to the wiener
deconvolution image to recover the original image.
After that the RMSE, PSNR, SSIM and visual perception
were analyzed for various images
DEBLU
RRED
IMAGE
INPUT
B
ESTIMATING
SPARSE
COEFFICIENT (α)
UPDATING
DICTONARY OF
THE IMAGE (D)
ESTIMATING THE
KERNEL VALUE K
KERNEL
&LATENT
IMAGE

3. RESULTS AND DISCUSSION
To implement the deblur algorithm is simulated using
MATLAB R2013a (8.1.0.604). The root mean square
error, power to signal noise ratio, structural similarity
index metric and visual perception were analyzed for
various images. From the analysis, it is observed that the
deblurring were efficiently performed.
Also carry out experiments with images blurred by
randomly generated kernel. The existing deblurring
algorithms are usually developed to deal with motion
blur problems in which the kernels are oriented and
simple. However, the camera shakes are complex and
cannot be modeled well with simple blur kernels. This
algorithm is able to recover the latent image with more
details and better contrast.
The initial kernel K0 is set to be the Gaussian kernel with
σ =1, and Γ is set as 1 and identity matrix I. The colour
images are used for experiments and crop a small portion
(e.g. 512×512 pixels) of the tested image to estimate
kernel using the algorithm as given in Chapter 2.The
regularized filter algorithm has been used to reconstruct
image I. The ﬁnal deblurred image can be recovered once
the deblur kernel is estimated.
(a) (b) (c)
Fig.2.Experimentel results of deblurring algorithm.(a)
blurred image (original size is 256 × 256);(b) deblurred
image 1;(c)final deblurred image
3.1 Performance Measurement
The root mean square error(RMSE), power to signal
noise ratio(PSNR), structural similarity index
metric(SSIM) and visual perception were analysed for
various images. From the analysis, it is observed that the
deblurring were efficiently performed for the use sparse
representation of the image. If the accuracy of the
estimated kernel is improved at each iteration, the
proposed algorithm will be ﬁnd a reasonably good
solution. Further reducing the RMSE comparable to other
methods.
Table -1: RMSE VALUES UNDER DIFFERENT
ALGORITHMS
Image Fergus
[11]
Shan
[12
Zhe
Hu
[13]
Deblur
Image(1)
Deblur
Image(2)
Barbara 5.53 7.02 4.61 3.51 1.27
Koala 5.41 6.57 5.10 3.21 1.06
Castle 1 7.87 7.46 6.73 3.12 1.05
Table -2: PSNR VALUES UNDER DIFFERENT
ALGORITHMS
Image Fergus
[11]
Shan
[12]
Zhe
Hu
[13]
Deblur
Image(1)
Deblur
Image(2)
Barbara 33.27 31.20 34.85 37.21 46.03
Koala 33.46 31.77 33.97 37.87 47.54
Castle 1 30.21 30.67 31.57 38.23 47.57
RMSE and PSNR comparison for different deblurring
methods shown in the table. The experiments are
conducted using four test images, namely Barbara, koala,
castle1.
Table -3: SSIM VALUE OF IMAGES
Image Deblur
Image(1)
Deblur
Image(2)
Barbara 0.7354 0.5427
Koala 0.7592 0.5486
Castle 1 0.8124 0.6495
From the analysis, it is observed that the deblurring were
efficiently performed. Because of the ssim value should
be less than 1.

4. CONCLUSION
In this paper, we propose an effective deblurring
algorithm with dictionary learning using one single image
were simulated. By decomposing the blind deconvolution
problem into three portions deblurring and learning
sparse dictionary from the image, our method is able to
estimate blur kernels and thereby deblurred images.
Experimental results show that this algorithm achieves
favourable performance. In future the deblurring
algorithm is to be implement on FPGA with suitable
architectures
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