9. Results and discussion

In this work, we have applied the proposed image denoising technique, the first image denoising technique based on DT-CWT [12] and the second denoising technique and the two-stage image denoising by principal component analysis with local pixel grouping [25], on a number of digital images such as "House," "Lena," and "Cameraman." These images are degraded by additive white noise with different values of noise-level, σ. PSNR and SSIM values obtained from the application of the three mentioned techniques on the noisy images are listed in Table 1.


Figure 12. (a) Clean image (Cameraman.tif), (b) Noisy image with, (c) The denoised image by the proposed technique

Wavelets and LPG-PCA for Image Denoising http://dx.doi.org/10.5772/intechopen.74453 253

Figure 13. (a) Clean image (Monarch.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the

(the first stage) and denoised image by the proposed technique (the second stage).

first stage) and denoised image by the proposed technique (the second stage).

Table 1. PSNR (dB) and SSIM results of the denoised images for the different techniques.

9. Results and discussion

252 Wavelet Theory and Its Applications

Technique The first image

denoising technique based on DT-DWT [12]

In this work, we have applied the proposed image denoising technique, the first image denoising technique based on DT-CWT [12] and the second denoising technique and the two-stage image denoising by principal component analysis with local pixel grouping [25], on a number of digital images such as "House," "Lena," and "Cameraman." These images are degraded by additive white noise with different values of noise-level, σ. PSNR and SSIM values obtained from the

application of the three mentioned techniques on the noisy images are listed in Table 1.

Two-stage image denoising by principal component analysis with local pixel grouping [25]: first stage

Table 1. PSNR (dB) and SSIM results of the denoised images for the different techniques.

House (σ = 10) 34.7138 (0.8778) 35.4 (0.9003) 35.6 (0.9012) 36.1223 (0.9130) House (σ = 20) 31.6671 (0.8253) 31.8 (0.8084) 32.5 (0.8471) 33.0828 (0.8677) House (σ = 30) 29.8494 (0.7877) 29.3 (0.7225) 30.4 (0.8185) 31.2095 (0.8393) House (σ = 40) 28.5744 (0.8084) 27.3(0.6243) 28.9 (0.7902) 29.7344 (0.8084) Lena (σ = 10) 33.6767(0.9170) 33.6 (0.9218) 33.7 (0.9243) 34.0765 (0.9271) Lena (σ = 20) 30.0002 (0.8539) 29.5 (0.8346) 29.7 (0.8605) 30.5415 (0.8765) Lena (σ = 30) 27.9859 (0.8016) 27.1 (0.7441) 27.6 (0.8066) 28.3595 (0.8292) Lena (σ = 40) 26.6364 (0.7585) 25.4 (0.6597) 26.0 (0.7578) 26.8566 (0.7882) Cameraman (σ = 10) 32.7481 (0.8989) 33.9 (0.9261) 34.1 (0.9356) 33.6141 (0.9241) Cameraman (σ = 20) 28.9990 (0.8175) 29.8 (0.8320) 30.1 (0.8902) 29.7184 (0.8575) Cameraman (σ = 30) 27.1022 (0.7641) 27.3 (0.7395) 27.8(0.8558) 27.8174 (0.8151) Cameraman (σ = 40) 25.7866 (0.7241) 25.5 (0.6393) 26.2 (0.8211) 26.4954 (0.7826) Monarch (σ = 10) 32.9907 (0.9369) 34.0 (0.9522) 34.2 (0.9594) 34.0698 (0.9553) Monarch (σ = 20) 29.1114 (0.8811) 29.6 (0.8859) 30.0 (0.9202) 30.0384 (0.9145) Monarch (σ = 30) 27.0058 (0.8346) 27.0 (0.8071) 27.4 (0.8769) 27.7209 (0.8735) Monarch (σ = 40) 25.5973 (0.7950) 25.2 (0.7267) 25.9 (0.8378) 26.0832 (0.8293) Peppers (σ = 10) 33.4942 (0.9056) 33.4 (0.8909) 33.3 (0.8943) 33.7904 (0.9189) Peppers (σ = 20) 29.8124 (0.8424) 29.9 (0.8177) 30.1 (0.8413) 30.5252 (0.8743) Peppers (σ = 30) 27.7810 (0.7924) 27.5 (0.7332) 27.9 (0.7973) 28.4765 (0.8356) Peppers (σ = 40) 26.4045 (0.7507) 25.9 (0.6447) 26.7(0.7648) 26.9883 (0.8013) Paint (σ = 10) 32.5488 (0.9165) 33.5 (0.9280) 33.6 (0.9311) 33.3567 (0.9276) Paint (σ = 20) 28.5980 (0.8416) 26.8 (0.7467) 29.5 (0.8683) 29.4699 (0.8648) Paint (σ = 30) 26.6067 (0.7817) 26.8 (0.7467) 27.2 (0.8088) 27.2540 (0.8077) Paint (σ = 40) 25.2968 (0.7330) 25.0 (0.6590) 25.6 (0.7569) 25.6389 (0.7560)

Two-stage image denoising by principal component analysis with local pixel grouping [25]: second stage The proposed technique

> Figure 12. (a) Clean image (Cameraman.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the first stage) and denoised image by the proposed technique (the second stage).

Figure 13. (a) Clean image (Monarch.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the first stage) and denoised image by the proposed technique (the second stage).

These obtained results (Table 1) show clearly that the proposed technique outperforms the denoising technique based on DT-CWT proposed in [12] and the denoising approach based on LPG-PCA [25]. Figures 12–15 show four examples of image denoising using the proposed

These figures show that the noise corrupting the original images is sufficiently suppressed. Moreover, the proposed technique permits to obtain denoised images with good perceptual quality. In each of these figures, the image (c) is obtained after the first denoising stage in the proposed technique. In this image (c), some noise is still existing, whereas it is considerably reduced into the image (d) obtained after the second denoising step. In the following subsection, we will give the results obtained by applying the proposed technique, the LPG-PCAbased denoising technique [25, 27] and the DT-DWT-based denoising one to a number of grayscale images. Those results are in terms of SNR and MSE and are listed in Table 2.

House (σ = 10) SNR = 78.00, MSE = 21.96 SNR = 79.41, MSE = 15.88 SNR = 79.44, MSE = 15.75 House (σ = 20) SNR = 74.95, MSE = 44.29 SNR = 76.37, MSE = 31.97 SNR = 76.38, MSE = 31.92 House (σ = 30) SNR = 73.14, MSE = 67.31 SNR = 74.50, MSE = 49.21 SNR = 74.50, MSE = 49.21 House (σ = 40) SNR = 71.86, MSE = 90.28 SNR = 73.02, MSE = 69.16 SNR = 73.02, MSE = 69.14 Lena (σ = 10) SNR = 74.67, MSE = 27.88 SNR = 75.28, MSE = 24.17 SNR = 75.28, MSE = 24.19 Lena (σ = 20) SNR = 70.99, MSE = 65.02 SNR = 71.53, MSE = 57.40 SNR = 71.55, MSE = 57.19 Lena (σ = 30) SNR = 68.97, MSE = 103.39 SNR = 69.35, MSE = 94.87 SNR = 69.37, MSE = 94.36 Lena (σ = 40) SNR = 67.62, MSE = 141.07 SNR = 67.85, MSE = 134.09 SNR = 67.87, MSE = 133.35 Cameraman (σ = 10) SNR = 75.33, MSE = 34.53 SNR = 76.19, MSE = 28.29 SNR = 76.23, MSE = 28.06 Cameraman (σ = 20) SNR = 71.58, MSE = 81.88 SNR = 72.30, MSE = 69.38 SNR = 72.33, MSE = 68.80 Cameraman (σ = 30) SNR = 69.68, MSE = 126.72 SNR = 70.39, MSE = 107.48 SNR = 70.45, MSE = 106.00 Cameraman (σ = 40) SNR = 68.36, MSE = 171.56 SNR = 69.07, MSE = 145.72 SNR = 69.14, MSE = 143.51 Monarch (σ = 10) SNR = 74.94, MSE = 32.65 SNR = 76.02, MSE = 25.47 SNR = 76.01, MSE = 25.55 Monarch (σ = 20) SNR = 71.06, MSE = 79.78 SNR = 71.99, MSE = 64.45 SNR = 71.98, MSE = 64.53 Monarch (σ = 30) SNR = 68.96, MSE = 129.56 SNR = 69.67, MSE = 109.89 SNR = 69.68, MSE = 109.62 Monarch (σ = 40) SNR = 67.55, MSE = 179.20 SNR = 68.01, MSE = 161.05 SNR = 68.03, MSE = 160.25 Peppers (σ = 10) SNR = 76.07, MSE = 29.08 SNR = 76.65, MSE = 25.43 SNR = 76.63, MSE = 25.56 Peppers (σ = 20) SNR = 72.39, MSE = 67.89 SNR = 73.10, MSE = 57.61 SNR = 73.12, MSE = 57.43 Peppers (σ = 30) SNR = 70.36, MSE = 108.38 SNR = 71.05, MSE = 92.34 SNR = 71.07, MSE = 92.02 Peppers (σ = 40) SNR = 68.98, MSE = 148.80 SNR = 69.57, MSE = 130.09 SNR = 69.58, MSE = 129.58

Two-stage image denoising by principal component analysis with local pixel grouping [25]

The proposed technique

Wavelets and LPG-PCA for Image Denoising http://dx.doi.org/10.5772/intechopen.74453 255

technique.

Technique The first image denoising

[12]

technique based on DT-DWT

Table 2. SNR (dB) and MSE results of the denoised images for the different techniques.

Figure 14. (a) Clean image (Lena.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the first stage) and denoised image by the proposed technique (the second stage).

Figure 15. (a) Clean image (Peppers.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the first stage) and denoised image by the proposed technique (the second stage).

These obtained results (Table 1) show clearly that the proposed technique outperforms the denoising technique based on DT-CWT proposed in [12] and the denoising approach based on LPG-PCA [25]. Figures 12–15 show four examples of image denoising using the proposed technique.

These figures show that the noise corrupting the original images is sufficiently suppressed. Moreover, the proposed technique permits to obtain denoised images with good perceptual quality. In each of these figures, the image (c) is obtained after the first denoising stage in the proposed technique. In this image (c), some noise is still existing, whereas it is considerably reduced into the image (d) obtained after the second denoising step. In the following subsection, we will give the results obtained by applying the proposed technique, the LPG-PCAbased denoising technique [25, 27] and the DT-DWT-based denoising one to a number of grayscale images. Those results are in terms of SNR and MSE and are listed in Table 2.


Table 2. SNR (dB) and MSE results of the denoised images for the different techniques.

Figure 14. (a) Clean image (Lena.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the first

Figure 15. (a) Clean image (Peppers.tif), (b) Noisy image with, (c) The denoised image by the proposed technique (the

stage) and denoised image by the proposed technique (the second stage).

254 Wavelet Theory and Its Applications

first stage) and denoised image by the proposed technique (the second stage).

Those results show that the proposed technique outperforms the two other techniques (the LPG-PCA-based denoising technique [25, 27] and the DT-DWT-based denoising one [12]). In fact the proposed techniques are the highest values of SNR and lowest values of MSE.

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