Research Article DENOISING PERFORMANCE OF LENA IMAGE BETWEEN FILTERING TECHNIQUES, WAVELET AND CURVELET TRANSFORMS AT DIFFERENT NOISE LEVEL R.N.Patel 1, J.V.Dave 2, Hardik Patel 3, Hitesh Patel 4 Address for Correspondence 1, 3 Department of Electronics and Communication Engineering, S.P.B.Patel Engineering College, Linch, Mehsana, Gujarat: 384435, India 2* Department of Electronics and Communication Engineering, Government Engg. College, Sector-28, Gandhinagar. 4 V. T. Patel Department of Electronics and Communication Engineering Charotar University of Science and Technology, Changa, Anand, Gujarat: 388421, India E Mail ratansing.patel@yahoo.com ABSTRACT In this paper we develop a method for denoising image, corrupted with random noise. The noise degrades quality of the images and makes interpretations, analysis and segmentation of image harder and the use of the time invariant discrete curvelet transforms for noise reduction is considered. We apply these digital transforms to the denoising of Lena image embedded in random noise with different noise level (σ = 1, 10, 20,, 500) and compare result with other denoising techniques [1,2,6,7]. The performances of both the transforms and filtering methods are compared in terms of Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Simulation time and the results are presented. I. INTRODUCTION In the real world signals do not exist without noise, which arises during image acquisition (digitization) and/or transmission. When images are acquired using a camera, light levels and sensor temperature are major factors affecting the amount of noise. During transmission, images are corrupted mainly due to interference in the channel used for transmission. Removing noise from images is an important problem in image processing. This noise removal takes place in the original time space domain or in a transform domain. In transform domain Fourier transform is used in the time-frequency domain and multiresolution transforms like wavelet/curvelet/contourlet transforms are used in the time-scale domain [4,11]. Denoising a given noise corrupted signal is a traditional problem in both statistics and in signal processing applications. Linear denoising methods are not so effective when transient non-stationary wideband components are involved since their spectrum is similar to the spectrum of noise, the basic idea that the energy of a signal will often be concentrated in a few coefficients in the transform domain while the energy of noise is spread among all coefficients in transform domain. Therefore, the nonlinear methods will tend to keep a few larger coefficients representing the signal while the noise coefficients will tend to reduce to zero. Denoising methods based on multiresolution transforms involves three steps: A linear forward transform, nonlinear thresholding step and a linear inverse transform. Wavelets are successful in representing point discontinuities in one dimension, but less successful in two dimensions. As a new multiscale representation suited for edges and other singularity curves, the curvelet transform has emerged as a powerful tool. The developing theory of curvelets predict that, in recovering images which are smooth away from edges, curvelets obtain smaller asymptotic mean square error of reconstruction than wavelet methods [4]. In this paper the image de-noising on different noise level and random noise added to image using both wavelet transform and curvelet transform. The performances of both the transforms and filtering methods are compared in terms of Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Simulation time and the results are presented. II. DENOISING USING CURVELET TRANSFORM Curvelets are based on multiscale ridgelets combined with a spatial band pass filtering operation to isolate different scales. Like ridgelets, curvelets occur at all scales, locations, and orientations shown in Fig. 1. However, while ridgelets all have global length and variable widths, curvelets in addition to a variable width have a variable length and so a variable anisotropy. The length and width at fine scales are related by a scaling law width = length 2 and so the anisotropy increases with decreasing scale like a power law. Curvelet transform is the new member of the evolving family of multiscale geometric transforms. It offers an effective solution to the problems associated with image denoising using wavelets. [7,8,9,10]. a. Materials and Methods The 512 512 Lena image was denoised using filtering method, curvelet and wavelet transforms. Random noise
was added to this image at different noise level shown in Fig. 2. Test image size of 2 n 2 n is used, where n=7, 8 and 9. A Noise factor of 1 to 500 is used for random noise. Set the percentage of coefficients used in the partial reconstruction is 0.5. Estimate noise level with robust estimator. Wrapping function [6] with a decomposition level of 8 was used for denoising the images using curvelet transform. Hard thresholding is applied to the coefficients after decomposition. For the coarse scale elements a value of 3*sigma is used and in case of fine scale elements a value of 4*sigma is applied and coefficients which exceed the specified level of thresholding were discarded and the remaining coefficients were used to reconstruct the image using the inverse wrapping function [6]. Fig.1. Spatial view point curvelets versus Frequency view point for different scale Fig. 2. Original image (top left) and other noisy Lena images with noise level σ = 1, 10, 20,, 500.
b. Algorithm Steps Following steps are involved in the denoising algorithm of Curvelet Transform: Compute all thresholds for cuvelets; Compute norm of curvelets; Apply curvelet transform to noisy image; Apply hard thresholding to the curvelet coefficients; and Apply inverse curvelet transform to the result of step 4 (to get its original image). For a noisy image first removed the noise through curvelet transform. Now find out the image background (Dim image not have fine details) the image with poor lighting. The morphological reconstruction filters which enhance the contrast are used to get a background of image. This chapter shows reconstruction by curvelet transform gives the satisfactorily result with poor lighting image. Through experiments analysis it is discovered that curvelet transform itself will not have the ringing and the radial stripe, but will appear in the threshold value denoising process [6,8]. So this article proposed an improved algorithm is as follows: Define original noise image is noisy_img, denoising image is restored_img, curvelet transform is C(t), twodimensional steady wavelet transform is F( t), N is odd number: For i = 1 to N restored_img = C (noisy_img); %Direct and inverse curvelet transform, threshold value denoising if (i mod 3 = 0) restored_img = F (restored_img); % Direct and inverse SWT end end III. IMAGE ASSESSMENT TECHNIQUES AND EXPERIMENTAL RESULTS [3,12,13] Traditionally, image quality has been evaluated by human subjects. This method, though reliable, is expensive and too slow for real world applications, so there is computational models that can automatically predict perceptual image quality which known as image quality assessment techniques. Where x(m,n) denotes the samples ) of original image, x( m, n) denotes the samples of distorted image. Where M and N are number of pixels in row and column directions, respectively, the techniques that used to assess the quality of images are: a. Equivalent Number of Looks (ENL) Another good approach of estimating the speckle noise level in a SAR image is to measure the ENL over a uniform image region [15]. A larger value of ENL usually corresponds to a better quantitative performance. The value of ENL also depends on the size of the tested region, theoretically a larger region will produces a higher ENL value than over a smaller region but it also tradeoff the accuracy of the readings. Due to the difficulty in identifying uniform areas in the image, we proposed to divide the image into smaller areas of 25x25 pixels, obtain the ENL for each of these smaller areas and finally take the average of these ENL values. A large value of the ENL indicates good denoising of the homogeneous region. The ENL is given by ENL= (1) b. Standard Deviation (SD) The large value of Standard Deviation means that image is poor quality. Fig. 2 and 3 shows that the standard deviation values of denoised images. As per the result, the SD values are lower for curvelet method and it is evident that curvelet based denoising method is superior to the other method in point of SD value. PSNR is very high and MSE is very low at σ = 1 and σ = 10 but at this value random noise is not exactly added with Lena image means original image is same as noisy image shown in Fig. 3(a) and Fig. 4(a). Curvelet Transform is more efficient for image denoising at value of sigma σ= 20 to 30 shown in Fig. 3(e), (f) and Fig. 4(e), (f). Finally we select the value of sigma σ= 20 because of denoising image having high PSNR and low MSE with respect to other values given in Table 1 and Table 2 for denoised images. SD is defined as follow: (2) Table 1. The MSE values for denoising 512 512 Lena image by Median & Weiner filtering, Wavelet, Curvelet and Modify curvelet transform with different value of σ Noise level 2 Mean Variance Mean SD= ENL Mean Square Error MF WF WT CT MCT σ = 1 16.15 8.556 1.702 1.513 1.499 σ = 10 36.81 25.78 38.226 27.535 27.354 σ = 20 91.20 79.12 77.520 51.034 50.751 σ = 25 131.88 122.43 98.717 63.9 63.705 σ = 30 176.82 173.46 97.9 76.9 75.55 σ = 35 233.93 233.47 134.53 88.68 88.275 σ = 40 298.20 304.66 156.49 102.20 100.89 σ = 50 450.59 470.4 196.81 127.61 125.99 σ = 100 1708.3 1839.5 337.21 254.06 252.44 σ = 200 6710.1 7258.9 567.98 513.67 505.31 σ = 500 41461 45161 1058.1 1502.6 1495.7
(a) (b) (c) (d) (e) (f) Fig. 3(a) Original Lena image (b) Noisy image (c) Denoised by median filter (d) Denoised by wiener filter (e) Denoised by curvelet transform (f) Denoised by modified CT (a) (b) (c) (d) (e) (f) Fig. 4(a) Original Lena image (b) Noisy image (c) Denoised by median filter (d) Denoised by wiener filter (e) Denoised by curvelet transform (f) Denoised by modified CT
Table 2. PSNR values for 512 512 denoised Lena image by Median & Weiner filtering, Wavelet, Curvelet and Modify curvelet transform with different value of σ Noise level PSNR(dB) MF WF WT CT MCT σ = 1 36.049 38.81 45.822 46.333 46.372 σ = 10 32.47 34.02 32.307 33.732 33.760 σ = 20 28.53 29.15 29.237 31.052 31.076 σ = 25 26.92 27.25 28.187 30.076 30.089 σ = 30 25.65 25.74 28.223 29.272 29.349 σ = 35 24.44 24.45 26.843 28.652 28.672 σ = 40 23.38 23.29 26.186 28.036 28.092 σ = 50 21.6 21.4 25.19 27.072 27.13 σ = 100 15.8 15.48 22.85 24.081 24.109 σ = 200 9.86 9.52 20.587 21.024 21.095 σ = 500 1.95 1.58 17.89 16.364 16.38 c. Mean Square Error (MSE) The simplest of image quality measurement is Mean Square Error (MSE). The performance of the proposed thresholding methods is evaluated and compared with that of soft, hard and cubic thresholding schemes using wavelets [14]. Gaussian noise was added to the classical Lena image. Multiple local thresholds are obtained using λ j. The curvelet coefficients are processed by thresholding functions and performance of denoising is evaluated using Peak Signal to-noise Ratio (PSNR) and Mean Square Error (MSE). PSNR is defined as the ratio of signal power to noise power. It basically obtains the gray value difference between resulting image and original image. MSE is given by: m 1, n 1 1 MSE= I( i, j) K( i, j) mn i, j= 0 (3) The large value of MSE means that image is poor quality. Table 1 shows the Mean Square Error values for denoising image using different method and also Fig. 5 shows MSE values for denoising image with different value of sigma (SD). 2 500 450 400 350 compare MSE with respect MF,WF,WT, CT and MCT median filter wiener filter wavelet transform curvelet transform modified CT Mean square error 300 250 200 150 100 50 0 0 5 10 15 20 25 30 35 40 45 50 standard deviation Fig. 5. Mean Square Error values for 512 512 denoised Lena image with different value of σ by Median & Weiner filtering, Wavelet, Curvelet and Modify curvelet transform.
d. Peak Signal to Noise Ratio (PSNR) Experimental results show that PSNR and MSE are improved with curvelet transform as compare to wavelet transform and other filtering method. Also, CT denoised image do not contain artifacts along edges. Table 2 shows PSNR values for denoised Lena image using different methods. Fig. 6 shows PSNR values for denoised image. Experimental work has demonstrated that curvelet denoising is more effective than wavelet as evaluated in terms of MSE Proposed method performs well both visually and in terms of MSE and PSNR for images contaminated by noise. A high quality image has higher value of Peak Signal to Noise Ratio and The PSNR is defined as: (4) Here, MAX I is the maximum pixel value of the image. The PSNR of the images denoised is compared using wavelet and curvelet transform for each type of noise mentioned above. Then the mean and standard deviation of each noise was calculated. 50 45 40 compare PSNR with respect MF,WF,WT, CT and MCT median filter wiener filter wavelet transform curvelet tarnsform modified CT PSNR in db 35 30 25 20 0 5 10 15 20 25 30 35 40 45 50 standard deviation Fig. 6. PSNR values for denoised Lena image by filtering method, WT, CT and modified CT with different value of σ Table 3. Simulation Times for 512 512 denoised Lena image by Median & Weiner filtering, Wavelet, Curvelet and Modify curvelet transform with different value of σ Noise level Simulation (elapsed) time(sec) MF WF WT CT MCT σ = 1 0.127 0.1358 34.518 32.241 31.988 σ = 10 0.112 0.143 35.944 32.356 32.320 σ = 20 0.113 0.134 35.023 32.885 32.105 σ = 25 0.111 0.135 37.9 33.463 32.743 σ = 30 0.112 0.136 43.976 42.7 36.34 σ = 35 0.114 0.138 42.671 39.036 32.56 σ = 40 0.112 0.141 43.49 32.115 37.36 σ = 50 0.117 0.147 38.868 32.448 32.967 σ = 100 0.120 0.136 44.566 33.409 32.637 σ = 200 0.121 0.144 12.68 32.497 32.491 σ = 500 0.108 0.139 12.405 32.03 32.74
In order to confirm the validity of curvelet transform improved denoising method, take Lenna gray image as the example. They are increased random noise separately at different values of σ from 1 to 500. Table 1, 2 and 3 shows curvelet improved denoising effects in comparison with others. To show effects clearly, we display the hat and the face region of Lena denoising images at different values of noise level σ,.e.g. Fig. 3. From Fig. 3 we found that the curvelet transform denoising effects were good, but meanwhile produced more radial stripes. By contrast, curvelet improved method changed this situation, but the denoising process correspondingly lost a part of edge characteristic and detail information due to adding wavelet transform to improved method. We could see that curvelet transform improved method is truly more effective than the other two methods. As shown in Table 1 and 2 Lena image was increased separately random noise σ = 1,10, 500, in all 11 groups data. Analyze the MSE and PSNR value change tendency of denoisong image among, Filtering method, Wavelet, Curvelet transform and curvelet improved method. Lena image in the situation of σ <35, PSNR value of curvelet transform improved denoising method is relatively high and MSE low. Table 3 shows that the improved curvelet denoising method take less simulation time compare to CT and WT but it take higher elapsed time compare to Filtering method. As per the result, the differences between PSNR values of denoised images for curvelet and wavelet methods are positive values, it is evident that curvelet based denoising method is superior to the wavelet method in point of PSNR value. IV. CONCLUSION The performance of the curvelet denoising method is evaluated and compared with Median, Wiener Filtering and Wavelet denoising schemes. The performance of denoising is evaluated using Peak Signal to- Noise Ratio (PSNR) and Mean Square Error (MSE) and Simulation time. PSNR is defined as the ratio of signal power to noise power. It basically obtains the gray value difference between resulting image and original image. As per the result, the difference between PSNR values of denoised images are 1.13dB higher (28.22dB for WT and 29.35dB for CT at σ=30.) at different noise level for curvelet method than the wavelet method, it is evident that curvelet base denoising method is superior to the wavelet method in point of PSNR value but curvelet transform is not effective at higher noise level i.e. σ = 500 of Lena image for denoising compare to wavelet methods. Curvelet method is performing effective with gray scale 2 n x2 n images not binary images in point of intensity level and also random size images. As per result, the MSE values (97.9 for WT and 75.55 for CT at σ=30) and Simulation time (43.98 for WT and 36.34 for CT at σ=30) are lower for curvelet than wavelet method, it is also evident that curvelet base denoising method is superior to the wavelet method in point of MSE value and Simulation time but curvelet transform is not effective at higher noise level i.e. σ = 500 of Lena image for denoising compare to wavelet methods. In short, the experimental results show the good performance of the modified curvelet method in comparison of Filtering methods and wavelet based decomposition and success to estimate and reduce noise from image in point of image quality assessment indexes. V. REFERENCES 1. R N Patel, Jignesh Patoliya, S D Joshi, Uniform Discrete Curvelet Transform for Image Denoising, International Conference E 3 C-2010, Nagpur. 2. 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