Noise Reduction Based on Multilevel DTCWT Using Bootstrap Method

ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3876 Noise Reduction Based on Multilevel DTCWT Using Bootstrap Method T.Eswar Reddy and K.M.Hemambaran Abstract- The main aim of this project is to reduce a noise introduced by new method which is known as bootstrap method. Image enhancement technique is clearly based on the random spray sampling technique. The output image of this exhibits noise with some unknown statistical distribution. Non enhanced image is consider to be free of noise or effected by certain levels of noise. By taking an advantage of highest sensitivity of HVS to change in brightness. The whole analysis is done on luma channel of both noise free and added noisy images. For giving an importance to directional content in human vision perception, the analysis is performed through the DTCWT. With the replacement of DWT we are using DTCWT for allowing data directionality. Every level of transform the standard deviation of noise free image is computed across the six orientations of the dtcwt. The obtained results show a map of directional structures present in the noise free image. According to data directionality in the dtcwt the shrunk coefficients and also the coefficients from the non enhanced image are then mixed. Finally by doing the inverse wavelet transform we are obtaining the resultant image as a noise reduced version of the enhanced image. Keywords: Bootstrap Method, Dual tree complex wavelet transform (DTWCT), Image enhancement, noise reduction, random sprays. I. INTRODUCTION Image enhancement is a very important application in digital world, as per consumer status it has never stopped evolving. A novel multi resolution denoising method is used to find a specific image quality problem this can be avoided by using image enhancement algorithm based on random spray sampling. Random sprays are implemented in spatial domain to collect a two dimensional points and used to sample an image support in place of other techniques, and have been previously used in works such as Provenzi [2], [3] and Kolas [4]. It can be implemented when image is Human Visual System (HVS). The existing Denoising algorithm is gives good noise reduction via coefficient shrinkage. And also the noise free image is introduced in the form of partial reference images. Having a reference allows the shrinkage process to be Manuscript received Nov, 2014. T.Eswar Reddy, ECE, SITAMS/JNTUA, Chittoor, India. K.M.Hemambaran, ECE, SITAMS/JNTUA, Chittoor, India data-driven and strong advantage of this method is to work based on Dual-tree Complex Wavelet Transform.. Finally, Proposing a Bootstrap method to prevent data loss in noise images compare to other methods i.e. existing denoised method and RSR(Random Spray Retinex) and RACE (combination of RSR and ACE(Automatic Color Equalization)) and main advantage in image analysis is that no assumptions have to be previously stated about the distribution of elements within the population. It is an empirical nonparametric technique commonly used to obtain several measures of a given statistic when the underlying statistical model is not known. Fig 1 shows traditional method for recovering noise free image from noisy image. Fig 1: Traditional Denoising Method The paper is organized as follows. Section II contains brief overview of Dual-tree Complex Wavelet Transform. After that, Section III and IV contain the proposed Denoising method and The Bootstrap Method, experimental results is implemented in Section V and finally, Section VI gives the conclusion. II. DUAL -TREE COMPLEX WAVELET TRANSFORM Discrete wavelet transform is introduced for application of digital image processing like image denoising to pattern recognition, image encoding and more. Being a complete and invertible transform of 2D data the Discrete Wavelet Transform gives rise to checker board pattern phenomenon. To avoid these two problems we use steerable filters introduced by Adelson and Freeman [19]. Which can be used to decompose an image into a Steerable Pyramid, by means of the Steerable Pyramid Transform (SPT) [8]? While, the SPT is an over-complete representation of data, data orientation will be shift invariant And it also having drawbacks that are perfect reconstruction is not possible and computational efficiency can be a concern. After SPT, thus a further development has been accomplished the Complex Wavelet Transform in order to compute the energy response by using the Hilbert pair of filters. To recovering the whole Fourier spectrum similar to SPT this transform needs to over complete by a factor of 4 means there are 3 complex coefficients for each real one. The CWT is also efficient and it can be computed through

separable filters, even though it still lacks the perfect reconstruction property. Later the Dual tree complex wavelet transform is proposed by Kingsbury and referred as work by Selesnick [21] for a comprehensive coverage on the DTCWT. The 2D DTCWT is implemented using the scaling and wavelet coefficients as shown in the below equations, =, =, =, =, (1) =, =,, =,, = (2) The low pass and high pass wavelet filters h and g is as shown below the chroma channel, and the whole operation is done only on the luma channel by using this wavelet space. Here we are using only the luminance channel because it does not provide any visible color. At final, we have to assume that the input is consider to be free of noise or affected by certain levels of noise. If we assume like this the original image contains some amount of information for reduction of noise successfully. For using the reference input image we have to reduce the noise in a noise affected image perfectly by using DTCWT. The algorithm for the proposed method is ALOGRITHM: Algorithm for Proposed Noise Reduction Method ( Here j is the decomposition level. When combining DTCWT coefficients the bases give rise to two sets of real and 2D oriented wavelets repeat for j=1 do for k=1 do end for for k=1 do is iteration dependent if + then Rank of Shrunk coefficients from else Coefficients from Fig. 2. Quasi-Hilbert pairs wavelets using in dual-tree complex wavelet transform. Even part shows on top and odd part on bottom and also each Pair is shown in a column The most important characteristic of wavelets is they are approximately Hilbert pairs and the coefficients deriving from one tree is imaginary and the other tree is real and also we obtain the desired 2D DTCWT. end if end for end for ) Inverse DTCWT until ssim (,, =concat (, ycbcr2rgb ( ) III PROPOSED NOISE REDUCTION METHOD Main idea of this method can be simplified as follows: user information conveys to the Human Visual System. According to data directionality, the proposed method using DTCWT produces wavelet coefficients by using those coefficients we have to shrink the coefficients from non enhanced image. The propose algorithm is as shown below. HVS has been more sensitive to changes occurred in the luma channel than the chroma channel [35]. And hence the proposed method first converts the original image into YCbCr. image and then the luma channel is separated from ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3877

ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3878 a normalized map of directionally sensitive weights for a given level j can be obtained as Where the choice of γ depends on j as explained later on. A shrunk version of the enhanced image s coefficients, according to data directionality, is then computed as + + Since the main interest is retaining directional information, we obtain a rank for each of the non-enhanced coefficients as, where ord is the function that returns the rank according to natural ordering. The output coefficients are then computed as follows Fig.3. Proposed method flowchart. Luma channels for both non enhanced and the enhanced images that are transformed using DTCWT and the obtained coefficients are enlarged. By using inverse DTCWT the output coefficients are transformed into the output image s luma channel and Computation indicated by the box in Fig. 3 is performed per level of the decomposition. Directional energy map is first computed as the standard deviation of sum-of-squares of the coefficients. A weight map is then obtained by using the Bootstrap Method. The even coefficients of the enhanced image are also ranked according to their magnitude. Weight map is used to scale the coefficients of the enhanced image. The resulting scaled coefficients and the coefficients from the non enhanced image are mixed according to the ranking. The process in is illustrated for even coefficients only, but it is repeated identically for odd coefficients. A. Wavelet Coefficients Shrinkage Assuming level j of the wavelet pyramid, one can compute the energy for each direction of the non-enhanced image k ε{1, 2,..., 6} as the sum of squares of the real coefficients and the complex ones Coefficients associated with non-directional data will have similar energy in all directions. On the other hand, directional data will give rise to high energy in one or two directions, according to its orientation. The standard deviation of energy across the six directions k = 1, 2... 6 is hence computed as a measure of directionality. = Since the input coefficients are not normalized, it naturally follows that the standard deviation is also non-normalized. The Bootstrap Method is thus applied to normalize data range and also for estimating standard errors. Such function is sigmoid-like and it has been used to model the cones responses of many species. The equation is as follows: BM(x, = Where x is the quantity to be compressed, γ a real-valued exponent and μ the data expected value or its estimate. Hence, where ord is the function that returns the index of a coefficient in =1,2,...,6 when the set is sorted in a descending order. The meaning of the whole sequence can be roughly expressed as follows: where the enhanced image shows directional content, shrink the two most significant coefficients and replace the four less significant ones with those from the non enhanced image. The reason why only the two most significant coefficients are taken from the shrunk ones of the enhanced image is to be found in the nature of directional content. For an content of an image to be directional, the responses across the six orientations of the DTCWT need to be highly skewed. In particular, any data orientation can be represented by a strong response on two adjacent orientations, while the remaining coefficients will be near zero. This will make it so that the two significant coefficients are carried over almost un-shrunk. To help for understanding the energies of the decompositions is as shown in equation 9. B. Parameter Tuning When dealing with functions with free parameters, a fundamental problem is finding optimum parameters values. While this can often be attempted with optimization techniques, such methods proved unfeasible in the case. To at least provide a reasonable default value for γj and J (the parameter of the Bootstrap method and the depth of the complex wavelet decomposition, respectively) tests were performed on three images from the USC-SIPI Image Database [37].We are taking Lenna image, Splash image and Girl image for showing the experimental results. In different rounds, Gaussian, Poissonian and Speckle noise was added to the luma channel of said images and the proposed noise reduction method was run with a J = 2 and values for γj varying from 5 to 10 in unit steps for the two levels of the decomposition. This allowed us to determine that values of γ1, γ2 and γ3 equal to 1 represent a reasonable choice, although non-optimal for all inputs. It should be noticed that

by doing so the Michaelis-Menten function is reduced to the Naka Rushton formulation [38]. Since J proved to be drastically more dependent on the input image than γj, it was impossible to determine a single optimum value. Therefore, J was left as the only user set parameter of the method, with reasonable bounds of Jmin = 1, Jmax = 2 The Bootstrap Method: IV PROPOSED METHOD The advantage of using bootstrap method with DTCWT for analyzing the image is, there is no assumption on previous statements about distribution of pixels within the original image. This bootstrap is commonly used for which is generally used for obtaining several measurements like mean and median values. This is used to collect number of data pixels in an image and then resample those collecting data pixels. The proposed data set is formed by the pixels of the original image is resample. Hence the several bootstrap data sets are generated for a previously number of times and also data collection is explained. The coefficients that are having in the bootstrap data sets are generally used to estimate mean and median values and also standard errors and unknown values. The noise is to be determined for a typical number of collected data sets and the bootstrapping value ranges from up to 300.The bootstrap standard error (SEBn) represents the standard deviation of replication of the bootstrap method SEBn= (18) Where b represents the measured parameters that is mean and median and so on. B represents the bootstrap number that means the number of random data sets and n represents the sub sampling used in this method and (19) The bootstrap coefficient of variation (CVBn) is estimated as follows CVBn = (20) Generally the bootstrap method is obtained for represents of this sampling areas and here we assume that the area of the whole image occupied is consider to be an object for analyzing purpose and it contains the total pixels of original image and hence the sampling area is considering as equal value of sizes. Every bootstrap data set is formed for measuring the sampling area of original image and the calculation of unknown statistical parameters that is mean and median etc. This will results that a large number of estimations of the unknown statistics parameters i.e. one for every bootstrap data range. It is used for determining the coefficient of variation (CVBn) and standard error (SEBn) for the particular sampling area is as shown in the below Figure 1. The minimum value for coefficient of variation or the standard error is defined as wit increasing the size of the sampling area and it is possible to determine the representative sampling area size. The advantage of the bootstrap method is its simplicity. It is straight forward way for estimating the standard errors of complex coefficients. And also it is an appropriate way for controlling and checking stability of the results. The general applications of bootstrap method are data missing problems and censored data. Estimation of Noise Statistics by Bootstrapping: Bootstrapping provides a practical procedure for estimating the parameters such as the mean and standard deviation etc. Depending on resampling process the parameters can be measured from an approximated distribution. This distribution is obtained from the available bootstrap data set. From the general Gaussian distribution we have to assume that a set of observations and it is implemented by using a number of resample from the bootstrap data that are all equal size. Every resample is obtained by sampling one by one witjh replacement from the original image pixel values. Another advantage of bootstrapping is it provides easy procedure for estimating the noise pixels in an enhanced image from complex transform coefficients of the observed bootstrap resampling pixel values. This bootstrap method is useful while satisfying the below two that is (i) the theoretical distribution of one statistic is unknown (ii) for statistical noise the size of the sample is not enough. Here we are using bootstrap method for estimating the noise intensity level according to the noise corrupted pixels. We are taking the noise pixel values while sample the image at the first time the noise intensity level is only one parameter of that image. Therefore the value of is to be estimate from the resampling original image. Our main idea of implementing the bootstrap method is more number of samples from the same pixels that can be efficiently replaced by resampling one that is by doing first sampling. By using the mathematical notations and equations let be the mean based on one random bootstrapping sample of size m. The estimated noise intensity level is obtained by selecting the median value of based on Z different bootstrapping samples where each sample is of size m. The following formula can be used to calculate different and based on calculated the can be obtained. Where is the absolute value of element in bootstrapping sample pixel. The estimation of is clearly obtained by using bootstrapping process. This methodology is a flexible and robust method for deriving sampling distributions and also standard errors. ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3879

ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3880 V EXPERIMENTAL RESULTS In this proposed Bootstrap Method with DTCWT the peak signal to noise ratio is increased compared to other denoising methods. Here we are adding different noise like Gaussian noise, poission noise and speckle noise for the enhanced luminance image. We are effectively reducing the all type of noises and increase value. The peak signal to noise ratio () is defined as, =10 The below figures shows the comparison results of DTCWT and DTCWT using Bootstrap Method with different noise affected images. EXISTING METHOD: Lenna image: Figure 5: Input image poission noise image Denoised luminance image Denoised RGB image PROPOSED METHOD: Lenna image: Figure 4: Input image, Gaussian noise image Denoised luminance image Denoised RGB image Girl image: Figure 6: Input image Gaussian noise image Denoised luminance image Denoised RGB image Girl image:

Figure 7: Input image Poission noise image Denoised luminance image Denoised RGB image The below table shows the comparisons of values of existing and proposed method of different images at different noises. TABLE 1: EXISTING METHOD Noise type Image name Noisy Gaussian Lenna Girl Splash 27.68 28.24 27.27 Denoised 33.90 35.39 37.15 VI CONCLUSION&FUTURE WORK In this paper, we are using wavelet based transforms for image denoising. Noise is one of the major problems in image processing that occurs while capturing the image and the image is transmitting through a channel. Here we are focused on different types of noises like Gaussian, poission and speckle noises. In this propose method we are using Bootstrap Method with DTCWT. The DTCWT using Bootstrap Method has several advantages over traditional denoising methods that are it is having shift invariance property and good directional selectivity. The above experimental results show that different images are affected by different type of noises. By using our proposed algorithm we have to denoised the noise affected images effectively and also calculate the image quality parameter which is known as value. Comparison results for existing and proposed methods are as shown in the above tables 1 and 2. The proposed method produces good quality output and removing noise without changing the directional structures in the image. Furthermore, improve the speed of the algorithm by avoiding iterations and also DTCWT is a tool for other activities such as image quality measures. Thus in future applied for audio and video signals denoising. Poission Lenna Girl Splash 28.50 29.08 30.26 Lenna 27.66 Speckle Girl 28.27 Splash 27.28 TABLE 2: PROPOSED SYSTEM Noise type Image name Noisy Lenna 27.68 Gaussian Girl 28.24 Splash 27.26 Lenna 28.50 Poission Girl 29.08 Splash 30.26 Lenna 27.66 Speckle Girl 28.27 Splash 27.28 33.92 34.38 37.13 33.89 35.47 36.98 Denoised 37.94 42.23 47.10 37.82 40.50 45.08 40.87 44.03 41.10 REFERENCES [1] Kingsbury, selesnick, Noise reduction based on partial-reference, Dual Tree Complex Wavelet Transform Shrinkage, IEEE Transaction on IMAGE PROCESSING, vol. 22, no. 5, May 2013 [2] M. Fierro, W.-J. Kyung and Y.-H. Ha, Dual-tree complex wavelet transform based denoising for random spray image enhancement methods, in Proc. 6th Eur. Conf. Color Graph, Imag. Vis., 2012, pp. 194 199. [3] E. Provenzi, M. Fierro, A. Rizzi, L. De Carli, D. Gadia, and D. Marini, Random spray retinex: A new retinex implementation to investigate the local properties of the model, vol. 16, no. 1, pp. 162 171, Jan. 2007. [4] E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, A spatially variant white patch and gray-world method for color image enhancement driven by local contrast, vol. 30, no. 10, pp. 1757 1770, 2008. [5] Ø. Kolas, I. Farup, and A. Rizzi, Spatio-temporal retinex-inspired envelope with stochastic sampling: A framework for spatial color algorithms, J. Imag. Sci. Technol., vol. 55, no. 4, pp. 1 10, 2011. [6] A. Chambolle, R. De Vore, N.-Y. Lee, and B. Lucier, Nonlinear wavelet image Processing: Variational problems, compression, and noise removal through wavelet shrinkage, IEEE Trans. Image Process., vol. 7, no. 3, pp. 319 335, Mar. 1998. [7] E. P. Simoncelli and W. T. Freeman, The steerable pyramid: A flexible architecture for multi-scale derivative computation, in Proc. 2nd Annu. Int. Conf. Image Process., Oct. 1995, pp. 444 447. [8] H. Rabbani, Image denoising in steerable pyramid domain based on a local laplace prior, Pattern Recognit., vol. 42, no. 9, pp. 2181 2193, Sep. 2009. [9] K. Li, J. Gao, and W. Wang, Adaptive shrinkage for image denoising based on contourlet transform, in Proc. 2nd Int. Symp. Intell. Inf. Technol. Appl., vol. 2. Dec. 2008, pp. 995 999. [10] Q. Guo, S. Yu, X. Chen, C. Liu, and W. Wei, Shearlet-based image denoising using bivariate shrinkage with intra-band and opposite orientation dependencies, in Proc. Int. Joint Conf. Comput. Sci. Optim., vol. 1. Apr. 2009, pp. 863 866. [11] X. Chen, C. Deng, and S. Wang, Shearlet-based adaptive shrinkage threshold for image denoising, in Proc. Int. Conf. E-Bus. E-Government, Nanchang, China, May 2010, pp. 1616 1619. [12] J. Zhao, L. Lu, and H. Sun, Multi-threshold image denoising based on shearlet transform, Appl. Mech. Mater., vols. 29 32, pp. 2251 2255, Aug. 2010. ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3881

ISSN: 2278 1323 All Rights Reserved 2014 IJARCET 3882 [13] N. G. Kingsbury, The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters, in Proc. 8th IEEE Digit. Signal Process. Workshop, Aug. 1998, no. 86, pp. 1 4. [14] D. L. Donoho and I. M. Johnstone, Threshold selection for wavelet shrinkage of noisy data, in Proc. 16th Annu. Int. Conf. IEEE Eng Adv., New Opportunities Biomed. Eng. Eng. Med. Biol. Soc., vol. 1. Nov. 1994, pp. A24 A25. [15] W. Freeman and E. Adelson, The design and use of steerable filters, IEEE Trans. Pattern Anal. Mach. Intell., vol. 13, no. 9, pp. 891 906, Sep. 1991. [16] N. G. Kingsbury, Image Processing with complex wavelets, Philos. Trans. Math. Phys. Eng. Sci., vol. 357, no. 1760, pp. 2543 2560, 1999. [17] I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, The dual-tree complex wavelet transform: A coherent framework for multiscale signal and image Processing, vol. 22, no. 6, pp. 123 151, Nov. 2005. [18] S. Cai and K. Li. Matlab Implementation of Wavelet Transforms. Polytechnic Univ., Brooklyn, NY [Online]. Available: http://eeweb.poly.edu/iselesni/waveletsoftware/index.html [19] E. H. Land and J. J. McCann, Lightness and retinex theory, J. Opt. Soc. Amer. A, vol. 61, no. 1, pp. 1 11, 1971. [20] D. Marini and A. Rizzi, A computational approach to color adaptation effects, Image Vis. Comput., vol. 18, no. 13, pp. 1005 1014, 2000. [21] R. C. Gonzales and R. E. Woods, Digital Image Processing, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002. [22] J. van de Weijer, T. Gevers, and A. Gijsenij, Edge-based color constancy, IEEE Trans. Image Process., vol. 16, no. 9, pp. 2207 2214, Sep. 2007. [23] USC-SIPI Image Database. (2009) [Online]. Available: http://sipi.usc.edu/database/ ABOUT THE AUTHORS T.Eswar Reddyreceived B.Tech degree from JNT University, Anantapur and is pursuing his M.tech degree from JNT University, Anantapur.Hisareas of interest are digital image processing and networking. Mr. K.M Hemambaran working as Assistant Professor in the department of ECE in SITAMS, chittoor. He received AMIE degree from institution of engineering (India) and he received M.tech degree from JNT University, Hyderabad. His areas of interest are Digital systems and Digital image processing.