 Open Access
 Total Downloads : 295
 Authors : Ms. Shraddha K. Hatwar, Prof A. L. Wanare
 Paper ID : IJERTV2IS100914
 Volume & Issue : Volume 02, Issue 10 (October 2013)
 Published (First Online): 25102013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Critical Performance Analysis and Comparison of Restoration for Diversified Field Images using Least Square Regression (LSR) Technique
Ms. Shraddha K. Hatwar, Prof A. L. Wanare
Professor in Electronics and Telecommunication, G. H. Raisoni college of Engineering and Management, Wagholi, University of Pune , Pune
Assistant Professor in Electronics and Telecommunication, Dr. D. Y. Patil School of Engineering, University of Pune, Pune
Abstract
In this Paper, we describe Least Square Regression Technique to design three algorithms. Automatic estimation of parameters and selection of restoration methods for diversified field images is done in proposed model. Image restoration plays an important role in computer vision and image analysis in special and transform domain. For comparative study, experimental results on test images demonstrate that the proposed technique performs better than the slandered algorithms on the basis of PSNR.

Introduction
Images are produced to record or display useful information in picture format. Due to imperfections in the process of capturing, the recorded image represents a degraded version of the original scene. Removing these imperfections is very difficult task form images many times. There exists a wide range of different degradations, which are to be taken into account, for instance noise, geometrical degradations, illumination, colour imperfections and blur. The main purpose of restoration is to obtain high quality of image from the low or degraded quality of image. In the use of image restoration methods, the characteristics of the degrading system and the noise are assumed to be known a priori [4]. The synthetic noises i.e. Salt and P epper, Gaussian, Speckle, and Poisson are used. In practical situations, however one may not be able to obtain this information directly from the image formation process.
The method of least square is to determine the best fit line to data. For this, it uses some calculus and algebra. To find out the best approximation to the data,
first task is to calculate the not only the solution for the least squares as the mean of some values having less variation or values having more variation will be same. Hence standard deviation is the solution to this to find out the errors easily. If the difference between mean and individual pixel value is more, ultimately the error will large and vice versa.
There exist so many types of images having their own characteristics. For example, images are taken from long distance. It contains the effect of electromagnetic radiation, variation of density of light. Natural Image: various natural sceneries, flower, plants, animals etc. are included in the natural images. Arial Image: Satellite images and Telescopic images are the part of Arial image. Medical Image: It includes Xrays, CT scan, and MRIs. It has the characteristics of human body or internal parts of a body [7]. Underwater image: it includes the images which are taken under the water which differ the refractive indices under water and on air.
On account of all these, application is designed which takes input as image and noise, it observes and analyses the type of image and the type of noise and recommends the most suitable restoration technique. To restore the images, so many techniques are available. Considering some filters, designing is done to restore or to deconvolve the degraded images. Least square regression technique is used to design the filters.

Background review
In general model of image restoration, the degraded image is restored automatically. First the image is browsed, and all blur and noises are occur in spatial domain; they are Gaussian, Poisson, Speckle, and Salt
and Pepper noise. According to model, Gaussian noise is distributed over signal while transmission which has bell shaped PDF. Salt & Pepper is an impulse noise; it
true image, degraded image is formed. That degraded version of image is gk [14].
g f h n
is generally caused by malfunctioning in picture
k k k k
(1)
element by manufacturing defects [9]. Speckle noise occurs in almost all coherent imaging system such as aperture radar imagery etc. The Poisson distribution is a discrete distribution that takes nonnegative integer value. After the addition of noise, the resultant image will be degraded version of the original one. This noisy degraded image when applied to any restoration filter, noise in that image may be removed partially. Image
browsed in the model can be colored or grayscale.
Where as usual we write for convolution and display the result in both the time domain and the frequency domain. Also, assume the sampling interval is one; otherwise sums in the time domain below need to be multiplied by and sums in the frequency domain need to be divided by . Therefore in frequency domain convolution is transformed to multiplication.
Then it is scaled to 256 256 and then applied to the working model. Each pixel in 256 256 image has two
Gj Fj .H j Nj
(2)
values of each dimension. For this model, three filters
i.e. Wiener Filter, Regularized Filter and Blind Deconvolution have designed. The quality of the
In the absence of noise, if we know the response functions of the apparatus we already know how to find the true image.
results was evaluated both visually and in terms of
PSNR, Mean Square Error (MSE). Detailed comparisons of filtering with different distortion metrics like ISNR, SC, NAE, AD, MD and NCC were
F Fj .H j
j
j
H j
(3)
evaluated, and analyzed that the proposed model yields significantly. Designed model for the restoration purpose is mentioned below:
Now we want to find the optimal Wiener filter, wk or Wj which, when applied to the measured signal and deconvolved by the instrument response, gives us an estimate of the true image:
F ' Gj .Wj
(4)
H
H
j
j
Note that it gives us the smeared signal from the system from the measured signal.
F
F
j
j
Now we have estimated function of image ' and
F
F
original image function . Sum of square of the
j
n 1
k 0
k 0
j j
j j
difference is (F
F ' )2
. To get the minimum error
Figure 1. Model in MATLAB
Sum of square of the difference should ideally be zero
E (F F )
E (F F )
n1
' 2
j j
Parameter values are shown in this above model. Also by calculating maximum or minimum value, this shows the suitable filter for the combination of image as well as noise. Here blur as well as Gaussian Noise has added.
and minimum as possible. Hence minimized. We have to minimize
n1
n1
E ( Fj .H j Gj .Wj )2
k 0 H j H j
k 0 is
(5)

Restoration Techniques

Wiener Filter Technique
Let the function of original image is fk . Here is some response function of the system hk . Synthetic noise has added to the system of each image. Let the added noise be nk . As the result of the processing of
Hence we have tried to minimize this equation for the implementation of wiener filter using least square regression technique.

Regularized restoration Technique
Regularized restoration provides results similar to Wiener filter but is justified by a very different viewpoint. Less prior information is require to apply regularized restoration. We have established a
technique for kernel based, regularized least squares regression methods, which uses the nonzero value for given conditions of the associated integral operator as a complexity measure [15]. We then use this technique to derive learning rates for these methods. Here, it turns out that these rates are independent of the exponent of the regularization term.
Given a training set ((x1, y1)….(xn , yn )) sampled from some unknown Point Spread Function (PSF) P on N*N matrix, the goal of least squares regression is to find a function R.
Here capital letters are used to indicate the Fourier transform of images. The information available in blind deconvolution is g(x,y) i.e. observed image and it is usually required to recover the original image f( x, y). The additional assumptions should be taken in the form of some a priori knowledge of either the object or the PSF to avoid an infinite number of possible solutions. In incoherent imaging, these assumptions usually take the form of a positive constraint on either the image or the PSF. Another constraint that is often employed is a support constraint, which depends on a blurred image being larger than either the true image or
RE,P ( f ) E( y, f (x))dp(x, y)
(6)
the psf. In practice a support constraint is implemented by restricting the extent of the recovered image and PSF to regions smaller than the extent of the blurred
Where E is the least squares error, i.e.
E( y,t) ( y t)
E( y,t) ( y t)
2
, is close to the optimal risk. Means when the value of error E is minimum the risk is minimum, when the value of risk increases the risk is also increases. Therefore at the value of infinity, risk R shows maximum value.
2
image. A final constraint which we employ in this technique is to assume that the spectrum of the unknown PSF is a lowpass filter, whereupon the convolution can be assumed to be a low resolution image of the true object. This is a powerful constraint since f(x, y) (function of true image) is common to all the blurred images [18].
By minimizing the error matric, image is
RE,P ( f ) R 'E,P ( f )  f f '  dpx
(7)
restored by blind deconvolution using the least squares as follows:
px – denotes the marginal distribution of p which
R ( f )
E  g(x, y) f (x, y) h(x, y) 2
is minimizer of E,P . f ' is well known regression C
function. We design the least square technique with
x, y
(11)
kernel based method. Hence observed verifiable risk is
n
n
R f (x) 1 (E( y , f (x ))
It indicates the deviation from being a perfect match to the observed convolution. We refer to EC as the convolutional error.
n
n
E ,V
i i
i1
(8)


Experimental Results
3.3. Blind Deconvolution
In many areas, the problem of distortion of image by unwanted point spread function (PSF) is occurred. In case of known PSF, the recovery of distorted image is relatively easy and straightforward. When original true image and PSF are unknown, Blind deconvolution is a significantly more demanding problem and occurs [13]. The basic model considered as
For the analysis of system, three images of each category Arial images, Medical images, Natural images, and Underwater images have taken.
(a) (b) (c) (d) (e) (f)
g(x, y) f (x, y) h(x, y) n(x, y)
(9)
where f(x,y) represents the true original image, h(x,y) is PSF, and g(x,y) the observed image. The term n(x, y) models the inevitable noise in the imaging process as an additive component. Symbol represents twodimensional convolution. Alternatively the convolution can be represented in the Fourier domain as
(g) (h) (i) (j) (k) (l)
Figure 2. Database of Images for Experimental Results (a) Telescopic, (b) Satellite, (c) Airplane, (d) X ray, (e) MRI, (f) CTScan, (g) Animal, (h) Lena, (i)
G(u, v) F(u,v)H (u,v) N(u,v)
(10)
Waterfall, (j) Fish 1, (k) Fish 2, (l) Fish 3
TABLE I
PSNR VALUES OF FILTERS FROM DIVERSIFIED FIELD IMAGES
Wiener Filter with Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
satellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
60.5284
58.375
59.245
59.258
59.094
60.989
59.899
60.055
59.2898
59.573
59.512
58.764
Poisson
63.329
58.127
60.426
65.058
60.791
63.201
59.576
61.622
62.2647
60.332
61.011
59.088
Speckle
59.864
56.074
57.529
59.807
58.302
59.273
56.058
56.944
57.2241
57.263
57.824
57.458
Salt &
64.5425
59.528
62.146
66.939
57.980
64.179
60.842
62.607
63.9179
61.619
62.54
60.954
Wiener Filter without Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
satellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
60.5419
58.385
59.224
59.245
59.103
60.977
59.905
60.062
59.2781
59.571
59.551
58.764
Poisson
63.329
58.127
60.426
65.058
60.791
63.201
59.576
61.622
62.2647
60.332
61.011
59.088
Speckle
59.8592
56.074
57.531
59.776
58.306
59.269
56.058
56.960
57.2158
57.260
57.822
57.461
Salt &
64.5425
59.528
57.531
66.939
63.023
64.179
60.842
62.607
63.9179
61.619
62.54
60.954
Regularized Filter with Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
saellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
56.0939
55.849
55.982
56.103
56.193
56.401
56.027
56.079
56.2186
56.017
56.038
55.925
Poisson
66.6428
60.938
63.530
70.712
65.851
68.161
63.861
65.633
66.4335
64.069
61.011
62.271
Speckle
52.6127
49.500
49.461
50.054
50.887
52.260
49.606
48.960
48.2038
49.702
50.044
51.157
Salt &
69.7565
63.869
66.506
71.909
56.094
70.332
66.696
68.608
69.0814
67.076
67.921
65.581
Regularized Filter without Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
satellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
60.5419
58.385
59.224
59.245
59.103
60.977
56.027
56.030
56.153
56.017
56.067
55.984
Poisson
63.329
58.127
60.426
65.058
60.791
63.201
63.861
65.633
66.4335
64.069
64.913
62.271
Speckle
59.8592
56.074
57.531
59.776
58.306
59.269
49.589
48.977
66.4335
49.637
50.007
51.121
Salt &
64.5425
59.528
57.531
66.939
63.023
64.179
66.696
68.608
69.0814
67.076
67.921
65.581
Blind Deconvolution with Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
satellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
56.4264
56.139
56.307
56.440
56.524
56.736
56.350
56.409
56.5501
56.342
56.367
56.228
Poisson
66.5059
60.812
63.397
70.586
65.665
67.997
63.719
65.482
66.2756
63.919
64.763
62.13
Speckle
52.946
49.829
49.792
50.388
51.219
52.598
49.939
49.294
48.5358
50.033
50.372
51.488
Salt &
69.556
63.673
66.313
71.915
56.421
70.212
66.496
68.402
68.8785
66.866
67.714
65.383
Blind Deconvolution without Least Square Regression
Arial Images
Medical Images
Natural Images
Underwater Images
telescopi
satellite
airplan
Xray
MRI
CT
Animal
Lena
Waterfal
fish 1
fisp
fisp
Gaussia
61.4721
58.434
60.229
62.320
61.209
61.624
60.068
61.186
61.4234
60.404
60.896
59.350
Poisson
65.3619
58.780
61.065
67.400
63.54
64.728
60.758
62.620
63.0801
61.340
62.039
59.283
Speckle
58.1923
54.832
55.000
55.656
56.980
54.144
55.064
54.462
53.6554
55.200
55.725
52.953
Salt &
68.1844
60.826
55.000
69.052
66.503
60.820
62.625
64.403
64.9852
63.360
64.140
62.647
Noises of Gaussian, Poisson, Speckle, Salt and pepper noise have added to all the images. These all results are taken on the basis of PSNR. For example, for Lena image, Gaussian noise is applied and PSNR=60.05dB is obtained as a result. The filter having large value of PSNR, considered as best filter for that combination of image and noise.
The figures shown in figure 3 in which the output of three images of each category are seperatly taken. On the basis of PSNR, the images have analysed. Here in all the gragh categorywise name of images in fig. 3 are mentioned on X axis and PSNR in db have shown on Y axis. Also on each image, four noises have mentioned. As Peak Signal to Noise Ratio, takes the ratio of Peak Signal power to the power of coruppted noise. It can be easily find with the help of MSE value. MSE measures the average of the squares of the error. PSNR in decible is
PSNR 20 log ( MAXI )
Figure 4. Performance of Wiener filter without least
square
Performance of Wiener Filter with Least Square and Without Least Square is almost same. i.e. the PSNR values of techniques are near about same.
10 MSE
(13)
4.2. Regularized Filter
Here MSE can be calculated as
1
1
N
N
M
MSE
MN
' 2

x

x
(x
(x
)
)
j,k j ,k
j 1 K 1
(14)
It is most easily defined via the mean squared error (MSE) which for two MÃ—N monochrome images i and k where one of the images is considered a noisy approximation of the other.
The Performance Analysis of individual filters with and without LSR is as follows:
4.1. Wiener Filter
Figure 3. Performance of Wiener Filter with Least
Square
Figure 3 shows the effect of Wiener filter on the various fields of images. For Xray images the result of Wiener comparatively gives good results. Broadly the Wiener filter gives better PSNR for Medical images. In almost all restored images the value of PSNR is large when Salt and Pepper noise is applied. Variation in results is high and gives wide range of PSNR value.
Figure 5. Performance of Regularized Filter with
Least Square
Regularized filter have greater PSNR for Salt and Pepper noise, also for Poisson noise. This filter gives average but better PSNR in the range 50 to 70 for all types of images and noises. This filter gives good results for Medical and Natural images.
Figure 6. Performance of Regularized filter without
Least square
For Arial Images and Medical Images The performance of Regularized Filter with Least Square is more than Without Least Square.
4.3. Blind Deconvolution
Figure 7. Performance of Blind Deconvolution with
least square
Blind deconvolution has better performance for Gaussian noise compared with the other filter, average PSNR= 56dB. It gives average results for all type of images.
Figure 8. Performance of Blind Deconvolution without
least square
Performance is better for the combination of Arial Images with salt and pepper noise as well as the combination of Arial Images with Poisson Noise. Also overall performance of Blind Deconvolution is better in case of Salt & Pepper Noise, Poisson Noise and Gaussian Noise is more as compared to without least square technique.


Conclusion
We have implemented three restoration techniques based on LSR to restore the diversified images (Medical, Arial, Natural, and Underwater). Performance of the Wiener filter, Regularized restoration and Blind deconvolution compared to each other using PSNR values. Proposed technique will
compare automatically to give suitable compilation of images and specific type of synthetic noise for optimum selection. LSR based restoration techniques are compared some state of art restoration techniques which are implemented only for single type of image and noise. After analysis of three techniques it is found better than some existing restoration methods.
10. References

Digital Image Processing By Gonzalez Woods and Eddins.

Digital Image Processing Using MATLAB by Gonzalez Woods and Eddins.

Image processing and data analysis by Fionn Murtagh University of Ulster Albert Bijaoui Observatoire de la Cote dAzur.

Mr. Salem Saleh Alamri, Dr. N.V. Kalyankar, A Comparative Study for Deblured Average Blurred Images, International Journal on Computer Science and Engineering Vol. 02, No. 03, 2010, 731733

Er.Neha Gulati, Er.Ajay Kaushik, Remote Sensing Image Restoration Using Various Techniques: A Review, International Journal of Scientific & Engineering Research, Volume 3, Issue 1, January2012.

Charu Khare, Kapil Kumar Nagwanshi, Implementation and Analysis of Image Restoration Techniques, International Journal of Computer Trends and Technology May to June Issue 2011

Ratnakar Dash, Parameters Estimation For Image Restoration, Dissertation report of Doctor of Philosophy

M. Sindhant Devi, V. Radhika Comparative approach for speckle reduction in medical images, International Journal of ART, Vol.01, Issue 01, pp711, 2011.

Deepa Kundur, Dimitrios Hatzinakos, A Novel Blind Deconvolution Scheme For Image Restoration Using Recursive Filtering, IEEE Transactions On Signal Processing, Vol. 46, No. 2, February 1998

Mr. Anil L. Wanare, Dr.Dilip D. Shah, Performance Analysis and Optimization of Nonlinear Image Restoration Techniques in Spatial Domain, International Journal of Image Processing (IJIP), Volume (6) : Issue (2) : 2012

Xiaoyang Yu, Yuan Gao, Xue yang, Chu Shi, Xiukun Yang, Image Restoration Method Based on Least Squares and Regularization and Fourth Order Partial Differential Equation , Information Technology Journal 9(5): 962967, 2010.

Carl W. Helstrom, Image Restoration By The Method Of Least Squares, Journal Of The Optical Society Of America Volume 57, Number 3 March 1967.

Nikolas P. Galatsanos, Aggelos K. Kasaggelos, Ronald
D. Chin, Least Square Restoration of Multichannel Images, IEEE Transaction on Signal Processing, Vol 39, No. 10. October 1991.

A. Khireddine, K. Benmahammed, W. Puech, Digital image restoration by Wiener filter in 2D case, Advances in Engineering Software 38 (2007) 513516

Nicol`o CesaBianchi, Applications of regularized least squares to pattern classification, Theoretical Computer Science 382 (2007) 221231

Punam A. Patil, Prof. R. B. Wagh, Review of blind image restoration methods, World Journal of Science and Technology 2012, 2(3):168170

AndrÂ´es G. Marrugo, Michal, Sorel, Filip, Sroubek, MarÂ´a S. MillÂ´an, Retinal image restoration by means of blind deconvolution, Journal of Biomedical Optics 16(11), 116016 (November 2011)

N.F. Law, R.G. Lane, Blind Deconvolution Using Least Squares Minimization, Optics Communications 128 (1996) 341352