Denoising of Fingerprint Images

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1 100 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

2 101 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

3 102 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 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 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).

4 103 S.NO SD PSNR values in db Random Noise Gaussian Noise S & P Noise DWT DCvT DWT DCvT DWT DCvT Speckle Noise DWT DCvT 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)

5 104 (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

6 105 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

7 106 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

8 107 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 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

9 108 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.

10 Apply the 2D FFT and obtain Fourier samples fˆ [n1, n2 ], n / 2 n1, n2 < n / 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 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

11 110 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 The quality of reconstructed image is usually specified in terms of peak signal to noise ratio(psnr). The PSNR values are calculated using eq 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 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

12 111 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.

13 112 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.

14 113 (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.

15 114 Table 6.1a Comparison of PSNR w.r.t SD for Gaussian noise (Lenna image) S.N. Standard deviation LCCT PSNR in db Gaussian noise DCvT LCWT DWT Table 6.1b Comparison of PSNR w.r.t SD for Speckle noise(lenna image) S.N. Standard deviation LCCT Table 6.1c Comparison of PSNR in db Speckle Noise DCvT LCWT DWT PSNR w.r.t SD for Salt & Pepper noise(lenna image) S.N. Standard deviation LCCT PSNR in db Salt & Pepper noise DCvT LCWT DWT

16

17 116 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.

18 117 (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.

19 118 Table 6.2a Comparison of PSNR w.r.t SD for Gaussian noise(building image) S.N. Standard deviation LCCT PSNR in db Gaussian noise DCvT LCWT DWT Table 6.2b Comparison of PSNR w.r.t SD for Speckle noise(building image) S.N. Standard deviation LCCT Table 6.2c Comparison of PSNR in db Speckle noise DCvT LCWT DWT PSNR w.r.t SD for Salt & Pepper noise(building image) S.N. Standard deviation LCCT PSNR in db Salt & Pepper noise DCvT LCWT DWT

20

21 120 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.

22 121 (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.

23 122 Table 6.3a Comparison of PSNR w.r.t SD for Gaussian noise(textured image) S.N. Standard deviation LCCT PSNR in db Gaussian noise DCvT LCWT DWT Table 6.3b Comparison of PSNR w.r.t SD for Speckle noise(textured image) S.N. Standard deviation LCCT Table 6.3c Comparison of PSNR in db Speckle noise DCvT LCWT DWT PSNR w.r.t SD for Salt & Pepper noise(textured image) S.N. Standard deviation LCCT PSNR in db Salt & Pepper noise DCvT LCWT DWT

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