Image Denoising Using Spatial Adaptive Thresholding

Transcription

1 International Journal of Engineering Technology, Management an Applie Sciences Image Denoising Using Spatial Aaptive Thresholing Raneesh Mishra M. Tech Stuent, Department of Electronics & Communication, BTIRT Sagar, M.P. Inia Megha Soni Assistant Professor, Department of Electronics & Communication, BTIRT Sagar, M.P. Inia Sueep Bauha Assistant Professor, Department of Electronics & Communication, BTIRT Sagar, M.P. Inia ABSTRACT In this paper, we escribe image enoising using wavelet transform an various existing algorithms using ifferent technique. The process of removing noise from an image is calle as noise reuction or enoising. In this paper, we have introuce some significant wavelet transforms for image enoising such as VisuShrink, BayesShrink, Bilateral an propose Spatial Aaptive thresholing techniques. Performance of noise reuction using propose technique is compare with several existing techniques such as VisuShrink, BayesShrink an Bilateral thresholing. It is measure on the basis of error metric such as Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) an in terms of visible quality of images. Keywors Wavelet Thresholing; DWT (Discrete Wavelet Transform); IDWT (Inverse Discrete Wavelet Transform); Image Denoising; VisuShrink Threshol; BayesShrink Threshol; Bilateral Threshol; PSNR (Peak signal to noise ratio); MSE (Mean Square Error) INTRODUCTION The central iea to wavelets is to analyze (a signal) accoring to scale. Imagine a function that oscillates like a wave in a limite portion of time or space an vanishes outsie of it. The wavelets are such functions: wavelike but localize. One chooses a particular wavelet, stretches it (to meet a given scale) an shifts it, while looking into its correlations with the analyze signal [8]. This analysis is similar to observing the isplaye signal (e.g., printe or shown on the screen) from various istances [1]. The wavelets are mathematical relations that examine the ata corresponing to the resolution or scale. They help in the stuy a signal at istinct resolutions in istinct winows. The wavelets offer certain avantages compare to Fourier transforms. The wavelets can also moel the music, speech, music, non-stationary stochastic signals an vieo. The wavelets may be use in applications such as human vision, turbulence, image compression, earthquake preiction an raar etc [5-6]. Donoho an Johnstone was the establish work on the filtering of AWGN with wavelet thresholing. From their behaviour an their properties, the wavelets contribute a significant responsibility in the image enoising an image compression [7]. The wor wavelet thresholing is ustifie that the ecomposition of the image or the ata in the coefficients of wavelet, comparing the component of coefficients by a specifie threshol value an shrink these coefficients nearby zero to get away the noise effect in the ata. The selection of a threshol is a significant aim of interest. He contributes a significant responsibility in the elimination of noise in the images as enoising more frequently evelops images, ecreasing the image sharpness. Precautions must be chosen to maintain the eges of the image enoising. There are several techniques for wavelet thresholing such as VisuShrink [], SureShrink [3] an BayesShrink [4], etc. An overview of this paper is organize as follows. Section shows wavelet thresholing. Section 3 illustrates image enoising using various existing thresholing techniques. Section 4 escribes propose Spatial Aaptive thresholing technique. Section 5 gives the simulation results. The final section raws the conclusions of this work. 3 Raneesh Mishra, Megha Soni, Sueep Bauha

2 International Journal of Engineering Technology, Management an Applie Sciences WAVELET THRESHOLDING Donoho an Johnstone was the establish work on the filtering of AWGN with wavelet thresholing. From their behaviour an their properties, the wavelets contribute a significant responsibility in the image enoising an image compression. While this thesis is base on the image enoising is iscusse in etail. The coefficients of wavelet calculate by the wavelet transform correspon to moify in the time series at a specific resolution. In stuying the time series at ifferent resolutions, then it is possible to filter the noise. The wor wavelet thresholing is ustifie that the ecomposition of the image or the ata in the coefficients of wavelet, comparing the component of coefficients by a specifie threshol value an shrink these coefficients nearby zero to get away the noise effect in the ata. The image is restore from the change coefficients. This process is calle as the inverse iscrete wavelet transform. Throughout thresholing metho, a coefficient of wavelet is comparison with a given threshol an is set to zero if its magnitue is below the threshol; or else, it is kept or change epening on the threshol rule. The thresholing separates between the coefficients because of the noise an those consisting of significant signal information. The selection of a threshol is a significant aim of interest. He contributes a significant responsibility in the elimination of noise in the images as enoising more frequently evelops images, ecreasing the image sharpness. Precautions must be chosen to maintain the eges of the image enoising. Earlier to the iscussion of wavelet thresholing techniques, it is essential to know the two common concepts of thresholing. They are soft thresholing an har thresholing [9]. The har thresholing can be characterize as T H = x for x t 0 in all other regions Where t is the value of threshol. The har thresholing (T H ) is shown in figure 1. -t t Fig 1: Har Thresholing Hence, all of coefficients whose magnitue is larger than the particular threshol value t continue equally they are an ifferent with magnitues below t are fixe to zero. It makes a area approximately zero when the coefficients are regare as negligible. Soft thresholing is whose the coefficients with larger than the threshol are ecrease to zero after compare with threshol value [9]. It is etermine as follows T s = sign x x t for x > t 0 in all other regions In practical, we can shows that the soft thresholing approach is better an gives more pleasant images. That is because the har thresholing approach is iscontinuous an gives abrupt recovery images. In aition, the soft thresholing approach gives a smaller amount of mean square error compare with the har thresholing approach. 4 Raneesh Mishra, Megha Soni, Sueep Bauha

3 International Journal of Engineering Technology, Management an Applie Sciences LL 3 HL 3 LH 3 HH 3 HL HL 1 LH HH LH 1 HH 1 -t t Fig : Soft Thresholing Now we can concentrate on the approach of thresholing mentione in above. For all these approaches the image is firstly applie on iscrete wavelet transform, which breaks own the image into several sub-bans [11-1]. It can be represente graphically as shown in figure 3. The sub-bans LH k, HH k, HL k are calle etails, where k is the scale varying from 1,, an is the total number of ecompositions. The sub-ban LL k is component of low resolution. The thresholing function is use to the etail components of all sub-bans to eliminate the coefficients, which a to the noise. Furthermore as the last step in the enoising, IDWT is use to restore the transform image from its coefficients. IMAGE DENOISING USING VARIOUS EXISTING THRESHOLDING TECHNIQUES There are several techniques for image enoising such as BayesShrink, VisuShrink an SureShrink etc. VisuShrink This VisuShrink has been evelope by Donoho. The purpose a threshol value t is proportional to the noise to the stanar eviation. It obeys the har thresholing approach. It is also calle as the universal threshol metho []. The universal threshol metho is efine by t = σ log n Where σ, the variance of the noise is present in signal, an n is the number of samples. The estimation of level to the noise σ was istinct base on the absolute average eviation an is efine as σ = meian g 1,k : k = 0,1, Where g 1,k is the etail coefficients of wavelet transform. 5 Raneesh Mishra, Megha Soni, Sueep Bauha

4 International Journal of Engineering Technology, Management an Applie Sciences VisuShrink oesn t reucing the square mean error. It can be consiere that as threshol selectors for general use that emonstrate near optimal minimum error an insures with a high probability that the computes are as smooth as the real unerlying functions. But, VisuShrink is known its performance to retrieve images that are excessively smoothe because the coefficients of too many remove by the VisuShrink an it can t remove speckle noise. It can only compact with an Aitive White Gaussian Noise. VisuShrink also followe global thresholing approach. SureShrink The SureShrink approach base on Stein s Unbiase Risk Estimator (SURE) was introuce by Donoho an Johnstone. SureShrink is a collection of SURE threshol an universal threshol. This approach etermines the threshol value t for every resolution level, which calle as epenent thresholing level [3]. The aim of this approach is to reuce mean square error an is given by n MSE = 1 z x, y s(x, y) n x,y=1 Where s(x, y) is the original signal, z x, y is the estimate signal an the size of the image or number of samples is n. In the empirical wavelet coefficients, SureShrink ecreases noise by thresholing. It is efine as t = min (t, σ log n) Where the noise variance is σ, t is the value that reuces SURE an the size of the image or number of samples is n. It obeys the soft thresholing approach. The aaptive thresholing use here, such for each yaic resolution level; we assigne threshol level by the principle of reucing the SURE for estimates of threshol. It is aaptive smoothness, means it reconstructe image when the unientifie function contains abrupt changes in the image. BayesShrink This BayesShrink has been evelope by Chang, Yu an Vetterli. The aim of this approach is to reucing the Bayesian risk an hence it is calle as BayesShrink [4]. It obeys the soft thresholing approach an it is epenent on sub-ban, which means that thresholing is calculating resolution at each ban in the wavelet ecomposition. It is aaptive smoothness ust like that SureShrink approach. The BayesShrink t B approach is efine as t B = σ σ s Where the noise variance is σ, an the signal variance without noise is σ s. In figure 3 from sub-ban HH 1, the noise variance is estimate by the meian estimator. An aitive noise follows the rule w (x, y) = s( x, y) + n( x, y) Hence the signal an the noise are inepenent of each other, so that σ w = σ s + σ σ w can be calculate as The signal variance σ s is calculate as σ w = 1 n w x, y n x,y=1 σ s = max σ w σ, 0 6 Raneesh Mishra, Megha Soni, Sueep Bauha

5 International Journal of Engineering Technology, Management an Applie Sciences IMAGE DENOISING USING PROPOSED TECHNIQUE Block iagram of system moel using propose metho has been seen in figure 4. Block iagram can be ivie into two threshol level such as first level threshol an secon level threshol. System moel consists of various type of block such as noisy image, iscrete wavelet transform (DWT), BayesShrink threshol, Inverse iscrete wavelet transform (IDWT), Propose Metho an Denoise Image block. These blocks can be escribe in below. Base on figure 4, the system moel containe the present image enoising techniques, so we have fin how to improve multiple thresholing approach. Therefore the stuy of new aaptive spatially approach, we fin how to improve minimum complex aaptive approach. The motivation for fining this approach is to reuce the complexity require with this approach. Noisy Image DWT Thresholing Metho IDWT First Level Threshol Denoise Image IDWT Propose Metho DWT First Level Threshol Multiple ecompositions have shown important avantages in the illustration of signals, an it is use comprehensively in image enoising, image segmentation an image compression [4]. The natural image is infecte by Gaussian noise; it is a common ifficulty in signal processing. The iscrete wavelet transform has been an important tool for image enoising because of its power compaction property. Therefore the wavelet transform gives a small number of large an a large number of small coefficients. The wavelet transform of image enoising approach follows as: Calculate the noisy image using wavelet transform. The noisy image wavelet coefficients moifie accoring to the rule. Calculate the inverse wavelet transform. The two common concepts are thresholing such as soft thresholing an har thresholing. The best thresholing concept is soft thresholing because the har thresholing approach is iscontinuous an gives abrupt recovery images. In aition, the soft thresholing approach gives a smaller amount of mean square error; it is very effective an simple. Assume the original image is f i, i, = 1,.. N, it is enote M M matrix which has integer of power is. During the image transmission, the image x infecte by the noise n i an stanar eviation is σ. In the receiver sie, the noisy image g i is g i = f i + σ n i The aim is to calculate the image x from noisy image such that the minimum mean square error is calculates. Assume the iscrete wavelet transform (DWT) an inverse wavelet transform (IDWT) are w an w 1 respectively. The wavelet coefficients of matrix G having four sub-bans such as LL, LH, HL an HH respectively. These sub-bans are calle as etails. The inverse iscrete wavelet transform is Where P is the soft thresholing function. Secon Level Threshol Fig 4: Detaile Block Diagram of System Moel Using Propose Metho x = w 1 P 7 Raneesh Mishra, Megha Soni, Sueep Bauha

6 International Journal of Engineering Technology, Management an Applie Sciences Secon Level Threshol A new aaptive thresholing technique combines the avantages of thresholing technique an wavelet epenencies. An important wavelet coefficient is W f(x, y), where x an y inicates the imensions an P f(x, y) representing the prouct value, it is greater than equal to an aaptive threshol t (). The metho is efine as Calculate the iscrete wavelet transform of input image f to scales. Calculate the proucts P f(x, y) an aaptive threshol t (). Then threshol of wavelet coefficients is W f x, y = W f x, y P f x, y t 0 P f x, y < t Where = 1,,.. J, an = x, y Retrieve the image from threshol wavelet coefficients W x f(x, y) an W y f(x, y). So that wavelet transform is a linear transformation, the iscrete wavelet transform of a noisy image is given by W f = W g + W ε Where the original image of iscrete wavelet transforms is W g an the noise of iscrete wavelet transforms is W ε. Therefore Z = P f = W f W +1 f The histograms of Z will have a heavy positive tail because of its high epenencies existing between W f an W +1 f. A proper threshol t () can be etermine an impose on Z to eliminate the highly noise corrupte pixels an ientify the significant image structures. Suppose that the input image is Gaussian white noise an it is an ergoic stationary process. For the convenience of expression, we enote the DWT of ε by U x, y = W ε x, y = ε φ x, y, U is a Gaussian noise process with stanar eviation ς = φ ς = x, y φ = φ x, y xy p u, u +1 = 1 πς ς +1 1 ρ +1, e 1/(1 ρ +1, ) u ρ ς +1, u u +1 ς ς +1 + u +1 ς +1 Where p +1, is given by ρ +1, = ψ (x, y). ψ +1 x, y xy ψ x, y xy. ψ +1 x, y xy The scale proucts of U an U +1 is: V = U U +1 The pf of p(v ) is given as: 8 Raneesh Mishra, Megha Soni, Sueep Bauha

7 International Journal of Engineering Technology, Management an Applie Sciences 1 p v = πγ( 1 )ς ς +1 1 ρ +1, e (ρ +1, v / 1 ρ +1, ς ς +1 ) K 0 v 1 ρ +1, ς ς +1 The stanar eviation of V is: Values of probability Pr (c) = P = v c. k, Where c is the constant. μ f = E Z, μ ε = E V k = E v = E u u p +1, ς ς +1 μ g = E W g. w +1 g Since the noise ε is inepenent of the noiseless image g, it can be erive that μ g = μ f μ ε μ ε = p +1, ς ς +1 The ratio μ ε /μ g () is the intensity of noise against signal in the multiscale proucts Z This ratio can be use to aust the threshol t () impose onz. The multiscale proucts threshol is: t p = 5k 1 + μ ε μ g The aaptive threshol t () is intuitive an effective. When noise is much stronger compare with the image, the ratio is high. Therefore, the threshol t becomes sufficiently large to suppress the overwhelming noise. When the image is ominative, the ratio is small an the threshol is at an appropriate level to preserve the image instantaneous features while removing noise [10]. SIMULATION RESULTS The propose metho has been applie on original gray scale image such as Lena at istinct noise levels (stanar eviation ς = 10 an 15). Performance of noise reuction using propose metho is compare with several existing methos such as VisuShrink, BayesShrink an Bilateral thresholing. It is measure on the basis of error metric such as Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) an in terms of visible quality of images. To measure the performance of propose metho an it is compare with the VisuShrink, BayesShrink an Bilateral thresholing using Peak Signal to Noise Ratio (PSNR) which is efine as the ratio between the square of maximum fluctuations in the input image (R) an Mean Square Error (MSE), taking log of base 10. In other wors, the ratio between the maximum possible value (power) of an image signal an the power of infecte noise image signal. The Peak Signal to Noise Ratio (PSNR) is generally efine in terms of logarithmic ecibel scale. The PSNR is PSNR = 0log 10 R MSE Where MSE is the Mean Square Error between the enoise image an the original image an the maximum fluctuations in the input image is R. The Mean Square Error (MSE) is efine as the square of the average errors between the original image signal an noisy image signal. The Mean Square Error is MSE = 1 MN 9 Raneesh Mishra, Megha Soni, Sueep Bauha M N m=1 n=1 B x m, n x(m, n)

8 International Journal of Engineering Technology, Management an Applie Sciences Where M is the with of image, N is the height of image, x m, n is the original image an x(m, n) is the noisy image. Consier the Peak Signal to Noise Ratio has been obtaine for Lena image of istinct noise level using propose metho an ifferent existing methos. The higher value of PSNR means, the noisy image signal has been better recovere to compare the original image an better the using methos. This means Mean Square Error woul be minimum between the original image an noisy image. The propose metho etermines the application in enoising images those are corrupte throughout the transmission which is generally ranom in nature. From Table 1 an, it is observe that the propose metho is better performs compare with other thresholing methos having higher PSNR an lower MSE values for ifferent noise levels (stanar eviation ς = 10 an 15). Table 1 Comparison of PSNR an MSE of ifferent methos for noise level (stanar eviation σ = 10) Methos PSNR (B) MSE Noisy Image VisuShrink BayesShrink Bilateral Propose metho From figure 5, the propose spatial aaptive thresholing algorithm provies better performance compare with thresholing methos like VisuShrink, BayesShrink, an Bilateral threshol proviing a better PSNR an MSE values. Table Comparison of PSNR an MSE of ifferent methos for noise level (stanar eviation σ = 15) Methos PSNR MSE Noisy Image VisuShrink BayesShrink Bilateral Propose metho (a) Original input image (b) Noisy image (c) VisuShrink thresholing 30 Raneesh Mishra, Megha Soni, Sueep Bauha

9 International Journal of Engineering Technology, Management an Applie Sciences () BayesShrink thresholing (e) Bilateral thresholing (f) Propose thresholing Fig 5: shows the image enoising using various thresholing methos CONCLUSION In this paper, we escribe image enoising using wavelet transform an various existing algorithms using ifferent technique. The process of removing noise from an image is calle as noise reuction or enoising. In this paper, we have introuce some significant wavelet transforms for image enoising such as VisuShrink, BayesShrink an Bilateral thresholing techniques. After that we propose Spatial Aaptive thresholing technique for image enoising. This technique is combination of thresholing technique an wavelet epenencies, it is also less complex in comparison other techniques. The avantages of Spatial Aaptive thresholing technique is that it is better performs compare with other thresholing methos having higher PSNR an lower MSE values for ifferent noise levels an gives better visual image quality. By using propose technique, the PSNR an MSE in the image enoising are B an as compare to the other techniques. REFERENCES [1] Daubechies, Ten Lectures on Wavelets, Philaelphia, PA:SIAM. [] D. L. Donoho an I. M. Johnstone, Ieal spatial aaptation by wavelet shrinkage, Biometrika, vol. 81, no. 3, pp , [3] D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, an D. Picar, Wavelet shrinkage: Asymptopia, J. Roy. Statist. Assoc. B, vol. 57, no., pp , [4] S. G. Chang, B. Yu, an M. Vetterli, Aaptive wavelet thresholing for image enoising an compression, IEEE Trans. Image Process. vol. 9, no. 9, pp , Sep [5] R.C. Gonzalez an R.E. Woos, Digital Image Processing. n e. Englewoo Cliffs, NJ: Prentice-Hall, 00. [6] M.Vetterli an C. Herley, Wavelet an filter banks: Theory an esign, IEEE Trans. Signal Processing, vol. 40, pp. 07 3, Sept [7] M.K. Mihcak, Kozintsev, an Ramchanran, "Spatially Aaptive Statistical Moeling of Wavelet Image Coefficients an its Application to Denoising," Proc. IEEE International Conference on Acoustic, [8] Ming Zhang, Bahair K. Gunturk "Multi-resolution Bilateral Filtering for Image Denoising," IEEE transaction of Image processing, Vol. 17, NO. 1, pp , Dec [9] D.L. Donoho, "Denoising an soft thresholing," IEEE. Transactions. Information. Theory, Vo1.41, PP , [10] P. Bao an L. Zhang, Noise reuction for magnetic resonance images via aaptive multiscale proucts thresholing, IEEE Trans. Meical Imaging, vol., no. 9, pp , Sep. 003 [11] Pizurica, W. Philips, I. Lemahieu, an M. Acheroy, A versatile wavelet omain noise filtration technique for meical imaging, IEEE Trans. Me. Imag., vol., pp , Mar. 003 [1] Q. Pan et al., Two enoising methos by wavelet transform, IEEE Trans. Signal Processing, vol. 47, pp , Dec Raneesh Mishra, Megha Soni, Sueep Bauha