Denoising of Fingerprint Images

100 Chapter 5 Denoising of Fingerprint Images 5.1 Introduction Fingerprints possess the unique properties of distinctiveness and persistence. However, their image contrast is poor due to mixing of complex type of noise. This chapter presents results of denoising of such images using algorithm proposed in chapter 4 and existing algorithms like wavelets. The next section will briefly describe the background on fingerprints and objective of this chapter. Finally it is

101 shown that the denoising algorithm proposed in the previous chapter is superior, in recovering edges, and of the faint linear and curvilinear features of fingerprint images, than the existing algorithm. 5.2 Background and Objective Fingerprints [86] have distinctiveness and persistence, which are highly desirable qualities for biometric applications. However, finger print images are generally of low contrast, due to skin conditions and application of incorrect finger pressure. Also, they inherently contain complex type of noise, originating from two distinct sources. The set of assorted devices involved in the acquisition, transmission, storage and display of the image is one source. Noise arising from the application of different types of quantization, reconstruction and enhancement algorithms is the second source. It is certain that every imaging method inherently involves noise. However different imaging methods involve noise of different extents. The occurrence of noise gives an image a mottled, grainy, textured or snowy appearance. The fingerprint images [87-91,99,100], with such an appearance, are often mistaken for the terminations. It is hence essential to look for methods offering superior denoising of finger print images. 5.3 Methods Used

102 This chapter presents results on denoising of fingerprint images, using algorithm proposed (curvelet denoising) in chapter 4 and existing algorithms like wavelets. The relative performance of the two types of algorithms is explained in terms of peak signal to noise ratio using eq. 3.7. Four types of noise, viz. Random noise(noise with either uniform or normal distribution), Gaussian noise, Salt & Pepper noise and Speckle noise, are chosen for mixing with the fingerprint image. The fingerprint images were downloaded from National Institute of Standards and Technology (NIST) database. For each type of noise, the extent of mixing corresponded to the standard deviations of 0.1,0.15,0.2,0.25,0.3 and 0.35. 5.4 Results and Discussion The PSNR values for the reconstructed images corresponding to the four types of noise, and standard deviations of 0.1, 0.15, 0.2, 0.25, 0.30 and 0.35 for each type of noise, are summarized in Table 5.1 Table 5.1 PSNR for different types of noise w.r.t curvelet denoising (DCvT) and wavelet denoising (DWT).

103 S.NO 1 2 3 4 5 6 SD 0.1 0.15 0.2 0.25 0.3 0.35 PSNR values in db Random Noise Gaussian Noise S & P Noise DWT DCvT DWT DCvT DWT DCvT 22.66 25.99 22.69 25.99 20.1 20.4 20.81 24.7 20.75 24.06 20.4 21.5 19.45 23 19.24 22.66 19.4 22.6 18.47 22.07 18.06 21.39 18.4 21.9 17.66 21.37 17.11 20.3 17.6 21.2 17.01 20.82 16.3 19.34 17 20.6 Speckle Noise DWT DCvT 22.93 26.24 21.01 24.32 19.59 22.96 18.39 21.84 17.46 20.93 16.78 20.18 The information presented in Table 5.1 and in Figs. 5.1 and 5.2 demonstrates that the curvelet based denoising algorithm,that has been discussed in previous chapter out performs the existing denoising method, which is based on wavelet transform, in reconstructing the fingerprint images. Fig. 5.1 shows the images for different noise types, corresponding to standard deviation (SD) value of 0.3. Original Fingerprint image (a) (b) For Random Noise (c)

104 (a) (a) (b) For Gaussian Noise (b) For Salt & Pepper Noise (c) (c) (a) (b) (c) For Speckle Noise Fig. 5.1 Images corresponding to SD of 0.3 (a) Noisy (b) Wavelet reconstruction (c) Curvelet reconstruction. Fig. 5.2 shows plots of PSNR vs SD corresponding to the Curvelet and Wavelet transforms, for the four types of noise. For Random Noise

105 For Gaussian Noise For Salt & Pepper Noise Fig. 5.2 For Speckle Noise Comparative plots of PSNR vs SD for Curvelet (DCvT) & Wavelet (DWT) Transforms. Chapter 6 Denoising by Lossy Compression and Curvelet Thresholding 6.1 Introduction

106 A new denoising technique, by combining curvelet thresholding, discussed in chapter 4 and lossy compression, discussed in chapter 3, is developed and demonstrated here. In this technique, a new reversible, linear transform known as curvelet is used to map the noisy image into a set of transform coefficients, which are then thresholded and quantized. In this chapter practical implementations of proposed denoising technique is focused. The next section will discuss on background and problem formulation and section 6.4 demonstrates the algorithm of new denoising technique. The alternative algorithm presented in this chapter is proved to be better in denoising the images. 6.2 Background and Problem Formulation Consider a more general model and look into an area of image processing which has been rather successful, namely, image compression. Notably, sub band coding such as Embedded zerotrees of Wavelet (EZW) [67] and its variants have achieved high compression rate with good visual qualities. The fact that compression methods are able to capture important image features with fewer bits implies that they achieve an efficient modeling of the image. Where efficiency is quantified in terms of description complexity. On the other hand, an image of white noise is hard to compress for any coder, because there is no structural correlation or redundancy to exploit. Thus, a good

107 compression method can yield a suitable model for descriminating between signal and noise. The idea of using a lossy compression algorithm for denoising has been proposed in several works [92-94]. Continuing on this theme, one main purpose of this chapter is to explain and to further substantiate the theory that lossy compression can be appropriated for denoising. Most coders operate in transform domain such as wavelet or discrete Cosine Transform, and this is also what is assumed here. Specifically, by posing quantization as an approximation to an effective denoising, called curvelet thresholding, it has been showed that quantization of curvelet transform coefficients achieves denoising. Analogous to the thresholding method of denoising, in a typical transform domain lossy compression method, negligible coefficients are set to zero, creating what is called a zero-zone or dead-zone, and coefficients outside of this zone are quantized. Hence an appropriate quantization scheme (and hence compression) achieves denoising because it is an approximation to the thresholding operation. The problem formulation and proposed denoising method are shown in Fig. 6.1. Say the signal is fij,i, j = 1,..., N, where N is an integer power of 2. It is corrupted by additive noise and is observed as g ij = f ij + ε ij i, j = 1,..., N

108 Where ε ij are not dependent and identically distributed(iid) as normal N (0, σ 2 ) and is not dependent on f ij. The aim is to eliminate the noise and to derive an estimate fˆij of f ij,or to denoise g ij. The denoising operation is done in the curvelet transform domain of the observed corrupted signal. Fig. 6.1 Problem formulation and proposed method for denoising. The noisy observation is the signal with additive noise. Noise removal is obtained in the curvelet transform domain by a combination of softthresholding and quantizing the curvelet coefficients. 6.3 Proposed LCCT Denoising Algorithm The following steps are involved in the new denoising algorithm named as Lossy compression and Curvelet Thresholding(LCCT). 1. Corrupt the original image with the noise to get noisy image f.

109 2. Apply the 2D FFT and obtain Fourier samples fˆ [n1, n2 ], n / 2 n1, n2 < n / 2. 3. For each scale j and angle l, form the product U% j,l [n1, n2 ] fˆ [n1, n2 ]. 4. Wrap this product around the origin and obtain f%j,l [n1, n2 ] = W (U% j,l fˆ )[n1, n2 ], where the range for n1 and n2 is now 0 n1 < L1, j and 0 n2 < L2, j (for θ in the range ( π / 4, π / 4) ). 5. Apply the inverse 2D FFT to each f% j,l, hence collecting the discrete coefficients c D ( j, l, k ). 6. Compute threshold for curvelets. 7. Apply soft thresholding to the curvelet coefficients. 8. Quantize the coefficients with the proposed quantizer discussed in Chapter 3. 9. Entropy code the quantizer outputs. 10.Apply inverse operations to the result of step 9. Denoising of the images using Lossy Compression and Curvelet Thresholding(LCCT) is carried out with wrapping based curvelet transform. Soft- thresholding [64], is applied to the coefficients after decomposition. Coefficients that are less than the chosen threshold are discarded. The quantization step forces the compression to be lossy. The inverse curvelet transform is used to reconstruct the image. Denoising of the images using curvelet transform(dcvt) is carried out as explained in[17,95,97]. Denoising of the images using

110 Lossy compression and wavelet thresholding(lcwt)[96] is done by replacing curvelet transform with the wavelet transform in LCCT algorithm. Denoising of the images using wavelet transform(dwt), [65-67], is carried out with db5 wavelet, which is an integral part of the wavelet tool box. The Speckle noise, is chosen for mixing with the standard Lenna image. The extent of mixing corresponded to the standard deviations of 0.20, 0.25, 0.30, 0.35, 0.40, 0.45 and 0.50. The quality of reconstructed image is usually specified in terms of peak signal to noise ratio(psnr). The PSNR values are calculated using eq.3.7. 6.4 Simulation Results and Discussion The Plain(Lenna), Building and Textured images are considered and corrupted with Gaussian, Speckle and Salt & Pepper noises. The noisy images are denoised using LCCT, curvelet denoising (DCvT), Lossy Compression and Wavelet Thresholding (LCWT) and wavelet denoising (DWT) algorithms. Figs. 6.2, 6.4 and 6.6 show original, noisy, DWT, DCvT, LCWT and LCCT images corresponding to Lenna, Building and Textured images in which Gaussian, Speckle and Salt & Pepper noises are used with standard deviation of 0.50. Figs. 6.3, 6.5 and 6.7 show plots between standard deviation Vs PSNR for Lenna, Building and Textured images corresponding to LCCT, DCvT, LCWT and DWT for the Gaussian, Speckle and Salt & Pepper noises. The PSNR values for the reconstructed images corresponding

111 to the Gaussian, Speckle and Salt & Pepper noise for the standard deviations of 0.10, 0.15,0.20,0.25,0.30,0.35,0.40,0.45 and 0.50 are summarized in Tables 6.1a,b,c; 6.2a,b,c and 6.3a,b,c correspondingly for Lenna, Building and Textured images. From the Tables 6.1a,b,c; 6.2a,b,c; 6.3a,b,c and Figs. 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7, it is observed that in case of Plain(Lenna) and Textured images for Salt & Pepper and Speckle noises LCCT outperforms the LCWT, DCvT, LCWT and DWT algorithms, where as for Gaussian noise DCvT dominates the LCCT, LCWT and DWT algorithms. In case of Building image for higher standard deviations irrespective of the type of noise DCvT outperforms the LCCT, LCWT and DWT algorithms, where as in case of Salt & Pepper noise for low standard deviations LCCT outperforms the other algorithms. From the analysis it is clearly observed that reconstruction with LCCT is possible for the Plain and textured images corrupted with Salt & Pepper and Speckle noises. The LCCT algorithm is not suitable for reconstructing the images in case of Gaussian noise irrespective of type of image. In this chapter it is emphasized and showed that image denoising based on Lossy compression and Curvelet Thresholding is better compared to the existing techniques in case of plain and Textured images corrupted with Salt & Pepper and Speckle noises. Same is reflected in the results obtained and presented here. This technique can also be employed as a part of machine vision and automation algorithm and results would be better.

112 Fig. 6.2 (a) standard Lenna image, (b) noisy image obtained by adding Gaussian noise with standard deviation of 0.5, (c) wavelet denoised image, (d) curvelet denoised image, (e) LCWT denoised image, (f) LCCT denoised image. (g) noisy image obtained by adding speckle noise with standard deviation of 0.5,(h) wavelet denoised image, (i) curvelet denoised image,(j) LCWT denoised image, (k) LCCT denoised image. (l) noisy image obtained by adding salt & pepper noise with standard deviation of 0.5, (m) wavelet denoised image, (n) curvelet denoised image,(o) LCWT denoised image and (p) LCCT denoised image.

113 (a) (b) (c) Fig. 6.3 Standard deviation(sd) Vs PSNR corresponding to LCCT, DCvT, LCWT and DWT algorithms for Lenna image corrupted with (a) Gaussian noise, (b) Speckle noise and (c) Salt & Pepper noise.

114 Table 6.1a Comparison of PSNR w.r.t SD for Gaussian noise (Lenna image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 29.2014 27.7573 26.0674 24.4285 23.1314 21.9274 20.8787 20.0959 19.3762 PSNR in db Gaussian noise DCvT LCWT 29.9943 25.5810 27.9813 25.2262 26.3493 24.2559 24.7929 22.8319 23.5464 21.7065 22.3435 20.6449 21.1841 19.5787 20.3896 18.9225 19.6160 18.3300 DWT 27.1959 25.3272 24.0183 22.7446 21.7699 20.8475 19.8731 19.1796 18.4919 Table 6.1b Comparison of PSNR w.r.t SD for Speckle noise(lenna image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 29.7092 29.4764 28.8873 27.9977 27.0401 26.0257 25.1380 24.3259 23.5426 Table 6.1c Comparison of PSNR in db Speckle Noise DCvT LCWT 30.4852 25.8299 28.6030 25.6699 27.2629 25.5860 26.1839 25.4067 25.2160 25.0229 24.4392 24.3462 23.7294 23.5806 22.9895 22.8079 22.3874 22.1550 DWT 27.5429 25.7137 24.6209 23.7049 22.8748 22.2398 21.5725 20.9991 20.5430 PSNR w.r.t SD for Salt & Pepper noise(lenna image) S.N. Standard deviation 1 2 3 4 5 6 0.10 0.15 0.20 0.25 0.30 0.35 LCCT 27.9009 27.8322 27.9573 27.7998 27.8548 27.8745 PSNR in db Salt & Pepper noise DCvT LCWT 21.4368 24.8279 23.4764 24.7316 26.2753 24.8178 25.8593 24.6955 25.0616 24.7285 24.5318 24.7526 DWT 22.9363 24.8132 24.2198 23.5006 22.7255 22.2245

115 7 8 9 0.40 0.45 0.50 27.8499 27.864 27.8721 24.0161 23.6044 23.1982 24.7090 24.8131 24.6659 21.7432 21.3926 21.0048

116 Fig. 6.4 (a) Original Building image, (b) noisy image obtained by adding Gaussian noise with standard deviation of 0.5, (c) wavelet denoised image, (d) curvelet denoised image, (e) LCWT denoised image, (f) LCCT denoised image. (g) noisy image obtained by adding speckle noise with standard deviation of 0.5,(h) wavelet denoised image, (i) curvelet denoised image,(j) LCWT denoised image, (k) LCCT denoised image. (l) noisy image obtained by adding salt & pepper noise with standard deviation of 0.5, (m) wavelet denoised image, (n) curvelet denoised image,(o) LCWT denoised image and (p) LCCT denoised image.

117 (a) (b) (c) Fig. 6.5 Standard deviation(sd) Vs PSNR corresponding to LCCT, DCvT, LCWT and DWT algorithms for Building image corrupted with (a) Gaussian noise, (b) Speckle noise and (c) Salt & Pepper noise.

118 Table 6.2a Comparison of PSNR w.r.t SD for Gaussian noise(building image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 30.5768 26.9469 24.2760 22.2670 20.5455 19.2734 18.0643 17.1043 16.2755 PSNR in db Gaussian noise DCvT LCWT 31.4926 29.5449 27.9113 25.9160 25.2237 23.2526 23.1413 21.2686 21.3119 19.6547 19.9691 18.4277 18.6552 17.3189 17.6229 16.4158 16.7377 15.6767 DWT 30.8324 27.3034 24.6577 22.6141 20.8434 19.5108 18.2252 17.2142 16.3685 Table 6.2b Comparison of PSNR w.r.t SD for Speckle noise(building image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 30.7873 27.1252 24.6188 22.6539 20.8827 19.4864 18.2876 17.2332 16.2550 Table 6.2c Comparison of PSNR in db Speckle noise DCvT LCWT 31.1477 30.4162 27.4984 26.8029 24.9633 24.2598 22.9792 22.2871 21.1865 20.5020 19.7824 19.1470 18.5824 17.9151 17.5112 16.8731 16.5356 15.9174 DWT 30.5444 26.8956 24.4015 22.5250 20.7267 19.3844 18.2064 17.2172 16.2516 PSNR w.r.t SD for Salt & Pepper noise(building image) S.N. Standard deviation 1 2 3 4 0.10 0.15 0.20 0.25 LCCT 28.9902 29.1152 28.9488 28.9364 PSNR in db Salt & Pepper noise DCvT LCWT 20.2997 25.5615 21.3101 25.6115 22.9646 25.4402 31.9369 25.5415 DWT 20.5330 26.8991 28.5061 29.1422

119 5 6 7 8 9 0.30 0.35 0.40 0.45 0.50 28.8400 28.9005 28.7450 28.9760 29.0346 31.5625 31.3323 30.8977 30.6424 30.3904 25.4722 25.4884 25.5363 25.4765 25.6955 28.4802 28.1028 27.2865 26.5273 26.2197

120 Fig. 6.6 (a) Original Textured image, (b) noisy image obtained by adding Gaussian noise with standard deviation of 0.5, (c) wavelet denoised image, (d) curvelet denoised image, (e) LCWT denoised image, (f) LCCT denoised image. (g) noisy image obtained by adding speckle noise with standard deviation of 0.5,(h) wavelet denoised image, (i) curvelet denoised image,(j) LCWT denoised image, (k) LCCT denoised image. (l) noisy image obtained by adding salt & pepper noise with standard deviation of 0.5, (m) wavelet denoised image, (n) curvelet denoised image,(o) LCWT denoised image and (p) LCCT denoised image.

121 (a) (b) (c) Fig. 6.7 Standard deviation(sd) Vs PSNR corresponding to LCCT, DCvT, LCWT and DWT algorithms for Textured image corrupted with (a) Gaussian noise, (b) Speckle noise and (c) Salt & Pepper noise.

122 Table 6.3a Comparison of PSNR w.r.t SD for Gaussian noise(textured image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 31.3070 29.0221 26.6930 24.7262 23.0283 21.6502 20.3677 19.4055 18.5467 PSNR in db Gaussian noise DCvT LCWT 31.9951 26.7313 29.2632 26.1198 27.0007 24.9998 25.0559 23.5025 23.2726 21.9377 21.7949 20.6654 20.4145 19.4074 19.3450 18.5600 18.3209 17.7319 DWT 29.1506 26.7061 24.7235 23.0655 21.5196 20.2676 18.9228 17.9673 17.1103 Table 6.3b Comparison of PSNR w.r.t SD for Speckle noise(textured image) S.N. Standard deviation 1 2 3 4 5 6 7 8 9 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 LCCT 32.4420 32.2925 31.7737 30.7577 29.6802 28.7419 27.7623 26.9273 26.2893 Table 6.3c Comparison of PSNR in db Speckle noise DCvT LCWT 33.2460 27.1171 30.7260 27.0555 29.1358 27.0052 27.9267 26.8708 26.9475 26.6771 26.1042 26.3112 25.3916 25.9380 24.6371 25.4392 2.0859 24.9207 DWT 29.8269 27.8091 26.1797 24.9342 23.9575 23.0535 22.3268 21.8156 21.2689 PSNR w.r.t SD for Salt & Pepper noise(textured image) S.N. Standard deviation 1 2 3 4 5 6 0.10 0.15 0.20 0.25 0.30 0.35 LCCT 28.8635 28.6644 28.8183 28.7199 28.8940 28.8636 PSNR in db Salt & Pepper noise DCvT LCWT 21.2785 25.7948 22.5469 25.6825 25.7194 25.5987 27.0667 25.7269 26.3130 25.7209 25.5007 25.7321 DWT 22.4179 25.7958 25.3889 24.5199 23.5995 22.7707