**5.3 Image denoising**

508 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

(a) (b)

(c)

We have observed no distinguishing evidence among the noise level estimation methods until level six. After this level, rigresure method has produced better SNR values. And it is observed that rigresure preserve the second heart sound in PCG signals while the other methods destroying. This situation is clearly seen in Fig. 10. The signal part related to second heart sound taking place at around 0.7s in Fig.10a is not able to seen in Fig. 10b and Fig. 10c. This shows that the rigresure preserve the main characteristic of the signal.

A level-dependent scaling of the thresholds was used to remove Gaussian white noise from the signal. Although it could not found evidence that a single wavelet was the best suited for denoising PCG signal, some wavelets used in this study were slightly better than the others. We conclude that reasonable decomposition level is absolutely depending on the sampling frequency and the frequency band of the signal. Just in this study, the decomposition level of 5 produced reasonable results because the frequency band of a normal PCG signal is around 150-200Hz and the sampling frequency is 11.5KHz. Since the noise level method is one of the important parameter in wavelet denoising, it is examined for different levels. We have not seen any noteworthy differences in the methods from level 1 to level 6. After this level, rigresure method has showed superiority to the other methods in terms of SNR level. Consequently, it is determined that the wavelet type is not very

Fig. 10. The denoised signal using three different threshold rules at level eight.

Therefore, we can conclude that the rigresure is the better noise estimation method.

All digital images contain some degree of noise due to the corruption in its acquisition and transmission by various effects. Particularly, medical image are likely disturbed by a complex type of addition noise depending on the devices which are used to capture or store them. No medical imaging devices are noise free. The most commonly used medical images are received from MRI (Magnetic Resonance Imaging) and CT (Computed Tomography) equipments. Usually, the addition noise into medical image reduces the visual quality that complicates diagnosis and treatment.

Because the wavelet transform has an ability to capture the energy of a signal in few energy transform values, the wavelet denoising technique is very effective as stated previous parts. As stated previous sections, when an image is decomposed using wavelet transform, the four subimages are produced, approximation, horizontal details, vertical details and diagonal details. Fig. 11 represents a sample medical image which belongs to a patient having cranial trauma and its four subimages when decomposed for one level using DWT. This image has acquired from a BT device. A noise added MRI image and its denoised form using wavelet denoising procedure is given Fig. 12. The added noise has Gaussian distribution, and symlet6, decomposition level of two, hard thresholding are chosen as wavelet denoising parameters.

Fig. 11. Decomposition of a sample medical image; original, approximation, horizontal details, vertical details, and diagonal details in left to right.

Fig. 12. A noisy image having PSNR 62dB and its denoised version.

Signal and Image Denoising Using Wavelet Transform 511

The best PSNR is obtained at the decomposition level of two. As can be seen in Table 3, the result PSNR value is decreasing if the decomposition level getting higher. The wavelet transform concern the main component of the original signal when the decomposition level is increased. If the higher decomposition level is used, the thresholding can eliminate some coefficients of the original signal, as in 1D signal denoising process. Therefore, to increase the decomposition level too high will decrease the PSNR after an optimal level and also increase the complexity of decomposition. In further part of the study, the decomposition level is chosen as two because the performance of the DWT denoising obtained at this level. Another question about the performance of the wavelet denoising is if it is dependent on the content or the distribution of the coefficient of the image. We can answer the question by applying the denoising algorithm on different images. Table 4 represents the PSNR values

respect to the number of the test images given in Fig. 9 after the denoising process.

Denoised Image (level2)

> 73.2903 69.3305 71.7193 72.2531 69.5873 71.7282 70.6594 73.7535 71.3191 71.0798

> 71.4721 1.4230

The wavelet denoising techniques offers high quality and flexibility for the noise problem of signals and image. The performances of denoising methods for several variations including thresholding rules and the type of wavelet were examined in the examples in order to put forward the suitable denoising results of the methods. The comparisons have made for the three threshold estimation methods, wavelet types and the threshold types. The examinations have showed that most important factor in wavelet denoising is what the decomposition level

However, someone has not seen any noteworthy differences in the methods from level one to level six, after this level, rigresure method has showed a better performance than the other methods in terms of SNR level. Consequently, it is determined that the wavelet type is not very important if the oscillation number is not very low, the decomposition level is absolutely depends on the frequency band of the signal to be analyzed and its sampling frequency.

is rather than the wavelet type, threshold type or the estimation of threshold value.

Denoised Image (level3)

> 72.9250 68.4441 70.4829 72.4830 69.9803 71.4382 70.8403 74.2233 69.4574 69.1241

> 70.9399 1.8322

Denoised Image (level4)

> 70.3792 67.3593 68.8435 70.8092 69.2444 70.0891 69.8362 71.6437 67.9060 67.4048

> 69.3515 1.4656

Denoised Image (level1)

> 68.1252 67.3979 67.9648 67.9819 67.0273 67.8774 67.6268 68.1391 67.9712 67.9048

0.3521

Table 4. PSNR's respect to image number, mean and standart deviation.

Number Noisy Image

62.0974 62.1251 62.1140 62.0942 62.0974 62.1023 62.1138 62.0995 62.1224 62.1070

62.1069

0,176 67.8016

Mean Standard Deviation

**6. Conclusion** 

Quantitatively assessing the performance in practical image application is complicated issue because the ideal image is normally unknown. Therefore the rational approach is to use known images for the tests, as in other image processing applications, in order to test the performance of the wavelet denoising methods like one dimensional signal denoising. Figure 13 represents the medical test images to be used.

Here, we use again a classical comparison receipt based on noise simulation. The comparison can be realized on the result reconstructed image and the original image after adding Gaussian white noise with known power to the original signal. Then it will be computed the best image recovered from the noisy one for each method. Firstly, we should determine the effective decomposition level because the most important factor in wavelet denoising is decomposition level. For this purpose, a noise added image will be used to obtain how the performance is changing respect to the decomposition level. The recovering process is made on the test image given in Fig 11, on which a Gaussian noise added to be PSNR is 62dB. The noisy image and a sample recovered or denoised is given Fig. 12a and Fig. 12b, respectively. The PSNR values after denosing process is given Table 3. In this denoising process, the symlet6 and universal thresholding is chosen as mother wavelet and noise level estimator.

Fig. 12. Medical test images.


Table 3. PSNR values respect to decomposition level after DWT denoising.

Quantitatively assessing the performance in practical image application is complicated issue because the ideal image is normally unknown. Therefore the rational approach is to use known images for the tests, as in other image processing applications, in order to test the performance of the wavelet denoising methods like one dimensional signal denoising.

Here, we use again a classical comparison receipt based on noise simulation. The comparison can be realized on the result reconstructed image and the original image after adding Gaussian white noise with known power to the original signal. Then it will be computed the best image recovered from the noisy one for each method. Firstly, we should determine the effective decomposition level because the most important factor in wavelet denoising is decomposition level. For this purpose, a noise added image will be used to obtain how the performance is changing respect to the decomposition level. The recovering process is made on the test image given in Fig 11, on which a Gaussian noise added to be PSNR is 62dB. The noisy image and a sample recovered or denoised is given Fig. 12a and Fig. 12b, respectively. The PSNR values after denosing process is given Table 3. In this denoising process, the symlet6 and universal

Level PSNR

68.1196 69.3269 70.5006 70.7768 68.6232 68.8183 68.7272 69.8037 66.8912 66.3877

Table 3. PSNR values respect to decomposition level after DWT denoising.

Figure 13 represents the medical test images to be used.

thresholding is chosen as mother wavelet and noise level estimator.

Fig. 12. Medical test images.

The best PSNR is obtained at the decomposition level of two. As can be seen in Table 3, the result PSNR value is decreasing if the decomposition level getting higher. The wavelet transform concern the main component of the original signal when the decomposition level is increased. If the higher decomposition level is used, the thresholding can eliminate some coefficients of the original signal, as in 1D signal denoising process. Therefore, to increase the decomposition level too high will decrease the PSNR after an optimal level and also increase the complexity of decomposition. In further part of the study, the decomposition level is chosen as two because the performance of the DWT denoising obtained at this level. Another question about the performance of the wavelet denoising is if it is dependent on the content or the distribution of the coefficient of the image. We can answer the question by applying the denoising algorithm on different images. Table 4 represents the PSNR values respect to the number of the test images given in Fig. 9 after the denoising process.


Table 4. PSNR's respect to image number, mean and standart deviation.
