An Effective Renovation Approach For
Improving the Image Quality
A.Chithra and K.Vijaya Bhaskar
Department Of Computer Science and Engineering,
MNM Jain Engineering College, Anna University,
Chennai, India.Chizinfotech29@gmail.com
Abstract— Image Renovation is an innovative way to improve the image quality. The key task in
real-world applications entails in providing competent, stable and fast recovery algorithms which, in
a few seconds, evaluate a good approximation of a compressible image from highly incomplete and
noisy samples. To address these issues, several reconstruction strategies have been recently
proposed, which aim to recover the missing information. The proposed system addresses about the
compressed sensing image recovery problem using adaptive nonlinear filtering strategies in an
iterative outline, and proves the convergence of the resulting iterative scheme. The proposed
framework is fast, stable and yields very good renovation, even in the case of highly under sampled
image sequences.
Keywords— Image Renovation, Compressed Sensing, Non linear filter, Total variation.
I. INTRODUCTION
A.
Image Renovation
Image renovation presents a challenging problem in the field of image processing. There are many
situations where it is necessary to reconstruct images of objects from collected data. The collected data
will be noisy, and hence the images reconstructed from the data are poor in quality. This project addresses
the issues in the reconstruction of images from sparse and noisy data. The objective is to develop
algorithms for the reconstruction of images with improved quality. Mathematically, the reconstruction of
an image from noise data is a problem of solving a set of underdetermined equations. Compressed sensing
(CS) is a technique for finding a solution to underdetermined linear systems.
Image renovation issues mainly include denoising, edge preserving, inpainting and smoothing.
These issues can be addressed using iterative approach of reconstruction and filtering strategy. The noisy
image may include unwanted signals to be denoised. The edges of the image are often affected while
renovation process which leads to staircase effect. To avoid especially staircase effect the edges of the
image should be preserved. The missing information should be painted and smoothing the image will
provide higher efficiency. The proposed framework is fast, stable and yields very
140
good
renovation,
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
An Effective Renovation Approach For Improving the Image Quality
even in the case of highly under sampled image sequences.
B.
Compressed Sensing
Compressed sensing is otherwise known as compressive sensing, compressive sampling and sparse
sampling, is a technique for finding sparse solutions to underdetermined linear systems. Compressed
sensing is the process of acquiring and reconstructing a signal that is supposed to be sparse or
compressible. An underdetermined system of linear equations has more unknowns than equations and
generally has an infinite number of solutions. However, if there is a unique sparse solution to the
underdetermined system, then the Compressed Sensing framework allows the recovery of that solution. It
follows that signals that have a sparse representation in a transform domain can be exactly recovered from
these measurements by solving an optimization problem. Sparse signals are an idealization that we rarely
encounter in applications, but real signals are quite often compressible with respect to an orthogonal basis.
This means that, if expressed in that basis, their coefficients exhibit exponential decay when sorted by
magnitude. As a consequence, compressible signals are well approximated by sparse signals and the
compressed sensing paradigm guarantees that from linear measurements it can obtain a reconstruction with
an error comparable to that of the best possible terms approximation within the sparsifying basis.
II. RECONSTRUCTION APPROACH
A. Methodology
A new denoising method is developed based on ROF model [2], [4] in combination with a vector
field smoothing algorithm. First, the input image is decomposed into a bounded variation component
standing for geometrical and an oscillating component standing for textured structure and noise. In which,
the Chambolle‘s projection algorithm [1] is adopted to perform numerical computation. Next, the
oscillating component is smoothed by using an indirect method derived from the vector field smoothing.
Then, the sum of the bounded variation component and the smoothed oscillating component is
calculated to obtain the smoothed result.
The proposed system can be seen as a modification and improvement of the traditional edgepreserving regularization where the bounded variation components are used as the processed results while
regardless the oscillating components. Such an approach allows preserving fine structures. The
comparison shows that the new smooth method outperforms the ROF, as well as the standard median
filters.
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
141
A.Chithra and K.Vijaya Bhaskar
B. System Architecture
Fig. 1 Overall System Architecture
C. Detailed Description
Parameter Initialization
•
Signal
The signal object is to specify the initial value of any signal. The initialized signal value will be
consistent. The given signal can be associated with at most the signal object.
•
It‘s Fourier Transform
It decomposes a signal into its Constituent frequency. It transforms signal into its constituent
frequencies.
•
Gradient Field
It is mainly for shading recovery problem. They are switched on and off 1000s of time in the signal
image. The switching creates forces and gives rise to unwanted signals. It is used for shadow
removal and lightness [8].
Iterative Reconstruction
In various information processing tasks obtaining regularized versions of a noisy or corrupted
image data is often a prerequisite for successful use of classical image analysis algorithms. Image
restoration and decomposition methods need to be robust if they are to be useful in practice. In particular,
this property has to be verified in engineering and scientific applications. By robustness, we mean that the
142
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
An Effective Renovation Approach For Improving the Image Quality
performance of an algorithm should not be affected significantly by small deviations from the assumed
model. In image processing, total variation (TV)[3] is a powerful tool to increase robustness.
The proposed system provides a new iterative [5] approach to perform minimization via the wellknown Chambolle's algorith [1]. The implementation is then more straightforward than the half-quadratic
algorithm. The behavior of image decomposition methods is also a challenging problem, which is closely
related to anisotropic diffusion.
EROF (Extended ROF) leads to an anisotropic decomposition [7] close to edges improving the
robustness. It allows to respect desired geometric properties during the restoration, and to control more
precisely the regularization process. It also discusses why compression algorithms can be an objective
method to evaluate the image decomposition quality. This algorithm exploits a dual formulation of the
minimization problem, and uses a fixed point iteration to find a solution of the dual formulation.
Chambolle proves that these iterations are contractant, and thus converge to a solution with linear speed.
Chambolle also exposes two important extensions of this algorithm:
1) The regularization parameter lambda can be updated during the iterations in order to solve
the
L2
constrained problem (instead of Lagrangian regularization). This is very useful if you know the
level of noise that is pertubating your measurements.
2) A slight modification of the iterations can be used to solve any inverse problem y=A x if the
operator A involved is an orthogonal projector, meaning that A A^*=Identity (the row of your
operator are mutually orthogonal).
These two features makes this algorithm useful to solve compressed sensing with random orthogonal
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
143
A.Chithra and K.Vijaya Bhaskar
(e.g. Fourier) measurements using TV regularization [3]
Apply Filter and Display
The Filter Approach uses new adaptive median filters .It does the following operations: [8], [9], [2],[7]

Classifies noise.

Act by shifting a point wide window along the directions of the input image and replacing the
central value with the median of the ordered set inside the window.

This process involves the convergence property of the output image. By iteratively applying the
new median formula pixel by pixel until convergence, we obtain the result.
III. CHAMBOLLE ALGORITHM
Antonin Chambolle [9] describes in an iterative algorithm for the resolution of TV regularized [3]
denoising,
xtv = argmin_u 1/2 * norm(x-u,'fro')^2 + lambda*TV(u)
(the so called "Rudin-Osher-Fatemi" denoiser), where TV(u) is the discretized TV norm of an image. This
algorithm exploits a dual formulation of the minimization problem, and uses a fixed point iteration to find
a solution of the dual formulation. Chambolle proves that these iterations are contractant, and thus
converge to a solution with linear speed.
First we load an image:
n = 256;
x = double ( imread('lena.png') );
x = x(end/2-n/2+1:end/2+n/2,end/2-n/2+1:end/2+n/2);
Rescale the image
x = (x-min(x(:)))/(max(x(:))-min(x(:)))
Then we select a random set of p Fourier frequencies that are our measurements. For the problem to be
well posed, we need to keep also some low frequencies.
Number of measurement
p = round (n^2/4)
Random set of frequencies
sel = randperm(n^2); sel = sel(1:p)
Add some low frequencies
eta = 15;
A = zeros (n);
A(end/2-eta+1:end/2+eta,end/2-eta+1:end/2+eta) = 1;
144
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
An Effective Renovation Approach For Improving the Image Quality
A = fftshift(A);
A(sel) = 1; sel = find(A(:)); p = length(sel)
We now perform noisy compressive sampling measurements.
Noise level,
sigma = .005;
Measurements,
y = y(sel) + sigma*randn(p,1)
We can perform L2 reconstruction by simple zero padding.
Zero padd the frequencies
x1 = zeros(n); x1(sel) = y;
Inverse fourier transform
x1 = real( n*ifft2(x1) );
Display
subplot(1,2,1); imagesc(x);
axis image; axis off; title('Original');
colormap gray;
Some parameters for Chambolle's algorithm.
Step size for each iteration of Chambolle's algorithm,
tau = 2/8 ,the theorem tells us that 1/8 is ok, but in practice 1/4
also works.
Tolerance error for the iteration of Chambolle's algorithm
inner loop,
tol = 1e-5
Number of iterations of the algorithm
niter = 400
Maximum number of iteration of Chambolle's inner loop
niter1 = 20
Initial regularization parameter value
lambda = .1
Target L2 error (should be very close to the norm of the noise)
etgt = sigma*sqrt(p)
Steps of iteration of Chambolle's algorithm.
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
145
A.Chithra and K.Vijaya Bhaskar
Chambolle's iteration,
gdv = grad( div(xi) - x1/lambda );
d = sqrt(sum(gdv.^2,3));
d = repmat( d, [1 1 2] );
xi = ( xi + tau*gdv ) ./ ( 1+tau*d );
At last we update the value of the regularization parameter,
lambda = lambda * etgt / norm( y-fxcs(sel), 'fro' )
Finally display the result.
IV. NEW ADAPTIVE MEDIAN FILTER
Median filters [6] are well known nonlinear filters used in image
denoising problems. They act by shifting a (2l+1) * (2l+1) point wide window along the two directions of
the input image and replacing the central value with the median of the ordered set inside the window.
These filters enjoy the following minimum property: the output of weighted median filter acting on the set
{Ui,i = 1,2,...,(21+1)*(21+1)} can be defined as the value of minimizing,
L (U) = EWi/U - Uil .i
In [20] the authors have shown that the action of the iterated median filter can be obtained using only one
iteration of its recursive version. We have, therefore, applied the following recursive new median filter,
V. EXPERIMENT
We show some examples of images processed with this algorithm.
In the examples of Fig. 3 to which a noise of standard deviation with 9% has been added. The
original is a 256 × 256 square image with values ranging from 0 to 255. The CPU time for computing the
reconstructed images is in both cases approximately 0.9 seconds, on a Intel pentium dual processor with 2
Mb of cache. The criterion for stopping the iteration just consists in checking that the maximum variation
between pn i, j and pn+1 i, j is less than 1/100. Notice that this algorithm can very easily be parallelized.
146
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
An Effective Renovation Approach For Improving the Image Quality
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
147
A.Chithra and K.Vijaya Bhaskar
VI .CONCLUSION
The proposed system is a powerful algorithm by combining compressed sensing approach and
adaptive non linear filter techniques that can be used in a variety of applications like prediction, error
concealment, inpainting etc. Further, we believe that the algorithm presented in this paper for compressed
sensing can be extended to other interesting imaging and vision applications.
REFERENCES
[1]
Yongping
Zhang,
Approach to Image
Member
Denoising
IEEE,
Based on
Zhongkun
He, Rina Su, Shaojing Fan (2010) , ―An
Variational Decomposition in Combination with
Vector Field Filter‖ .
Leonid I. Rudin 1, Stanley Osher and Emad Fatemi (2005) ‗Nonlinear total variation based noise
[2]
removal algorithms‘.
Ivan Selesnick Ilker Bayram (2006) ‗Total Variation Filtering‘, The Connexions Project and
[3]
licensed under the Creative Commons Attribution License.
Donald Goldfarb and Wotao Yin (2007) ‗Parametric maximum flow algorithms for Fast totals
[4]
variation minimization‘ Department of Industrial Engineering and operations
Research, Columbia
University.
J. Bioucas-Dias and M. Figueiredo, ‗A new TwIST: Two step iterative shrinkage-thresholding
[5]
algorithms for image restoration‘, IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992–3004, Dec. 2007.
Y. Li and S. Osher, ―A new median formula with applications to PDE based denosing,‖
[6]
Commun. Math. Sci. , vol. 7, no. 3, pp. 741–753, 2009
Laura B. Montefusco, Damiana Lazzaro, and Serena Papi ‗Fast Sparse Image Reconstruction
[7]
Using Adaptive Nonlinear Filtering‘ , IEEE Transactions on Image Processing , Vol.20 , No.2, February
2011.
[8]
Graham D. Finlayson, Member, IEEE, David Connah, and Mark S. Drew, ‗Lookup-Table-Based
148
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
An Effective Renovation Approach For Improving the Image Quality
Gradient Field Reconstruction‘, IEEE Transactions on Image Processing , Vol.20 , No.10, October 2011.
[9]
Chambolle,
―An
algorithm
for
total
variation minimization and applications,‖ J. Math.
Imaging Vis. 20, 2004, pp. 89–97.
‫ ﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣ‬IJCI-2K10-63 ‫ﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣﻣ‬
ACS-International Journal in Computational Intelligence, Vol-3, Issue-1 Mar 2012
149