 Open Access
 Total Downloads : 1073
 Authors : Reeta Charde
 Paper ID : IJERTV1IS5476
 Volume & Issue : Volume 01, Issue 05 (July 2012)
 Published (First Online): 03082012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Comparison of Wavelet Denoising and Median Filter Denoising over AWGN Channel
Reeta Charde
EC Department,Indore Institute of Science and technology, Indore
Abstract
This paper presents approach towards Wavelet Transform and Median Filter for image reconstruction. In the past two decades, many noise reduction techniques have been developed for removing noise and retaining edge details in images. The primary goal of noise reduction is to remove the noise without losing much detail contained in an image. Wavelet transforms are specially used for compression, Denoising, Thresholding, Error reduction, reconstruction, and for image synthesis. There are different types of wavelets transform and filters are used for image reconstruction. For different value of signal to noise ratio (SNR), Bit Error Rate (BER), Root Mean Square Error (RMSE) and Peak Signal to Noise Ratio (PSNR) will change. We are using Wavelet and Median Filter for finding BER, RMSE and PSNR. The challenge is to find the best reconstruction methods for BER, RMSE, PSNR and a good perceptual result.
Keywords: WT, Image, Median Filter, SNR, RMSE, PSNR, BER, Reconstruction, Decomposition
Introduction
The objective of image reconstruction is to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form. Wavelet transform and median filter are used for image reconstruction & denoising, for that best perceptual result Phase Shift Key (PSK) technique is used. Phaseshift keying is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal. For that simply load a image then we have to convert image into binary data. This binary data convert into serial form then it can be modulate and then demodulate using PSK technique. Again we have to convert serial into parallel form. Inverse Wavelet Transform as well as median filter is used for image reconstruction. We get maximum PSNR and minimum RMSE using Median Filter as compare to inverse Wavelet Transform.
Wavelet Transform
A wavelet is a small wave which has its energy concentrated in time. It has an oscillating wavelike
characteristic & it as timescale and timefrequency analysis tools have been widely used in topographic reconstruction and still growing.
Discrete Wavelet Transform
Image Reconstruction with wavelet transform used 2D version of the analysis and synthesis filter banks. In the2D (image) case, the 1D analysis filter bank is first applied to the columns of the image and then applied to the rows. If the image has N1 rows and N2 columns, then after applying the 1D analysis filter bank to each column, two subband images are created, each having N1/2 rows and N2 columns; after applying the 1D analysis filter bank to each row of both of the two subband images, four subband images are generated, each having N1/2 rows and N2/2 columns.
Figure 1: One stage in multiresolution wavelet decomposition of an image
Two Dimensional Discrete Wavelet Transform (2D DWT)
The DWT is extensively used in its nonredundant form known as standard DWT. The filter bank implementation of standard DWT for images is viewed as 2D DWT. There are certain applications for which the optimal representation can be achieved through more redundant extensions of standard DWT such as WP and SWT. Image processing applications require twodimensional implementation of wavelet transform. Implementation of 2D DWT is also referred to as multidimensional wavelet transform in literature.
The implementation of an analysis filter bank for a single level 2D DWT is shown in figure.
Figure 2: Single level analysis filter bank for 2D DWT
This structure produces three detailed subimages (HL, LH, HH) corresponding to three different directionalorientations (Horizontal, Vertical and Diagonal) and a lower resolution subimage LL. The filter bank structure can be iterated in a similar manner on the LL channel to provide multilevel decomposition. Multilevel decomposition hierarchy of an image is illustrated in figure .
Figure 3: Multilevel decomposition hierarchy of an image with 2D DWT
Each decomposition breaks the parent image into four child images. Each of such subimages is of one fourth of the size of a parent image. The sub images are placed according to the position of each subband in the twodimensional partition of frequency plane as shown in above fig 4. The structure of synthesis filterbank follows the reverse implementation of analysis filterbank but with the synthesis filters. Figure shows original image of BabyGrow and its lower resolution, horizontal, vertical & diagonal images are presented of 1st decomposition.
Figure 4: Original Image
Figure 5: Lower resolution image
Figure 6: Horizontal Image
Figure 7: Vertical Image
Figure 8: Diagonal Image Haar Wavelet Transform
The Haar Wavelet is a certain sequence of rescaled "squareshaped" functions which together form a wavelet family.
Noise in Images
Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. It can be produced by the sensor and circuitry of a scanner or digital camera. Noisy image can be modeled as
Figure 9: Haar wavelet Transform
The Haar wavelet's mother wavelet function (t) & its scaling function (t) can be described as
Effects of Noise on Images
Where i, j = 1: N
Phase Shift Key (PSK) Modulation and Demodulation
Phaseshift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal. PSK modulation in Matlab can be simulated using the pskmod() function and demodulation can be performed using pskdemod(). The pskmod() produces a sequence of channel symbols (e.g. fs3, s3, s5, s6, s1, : : :g).
Figure 10: PSK Waveform Communication Channel
A communication channel is used to convey an information signal, for example a digital bit stream, from one or several senders (or transmitters) to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second.
Noise gives an image a generally undesirable appearance, the most significant factor is that noise can cover and reduce the visibility of certain features within the image. The loss of visibility is especially significant for lowcontrast objects.
Additive white Gaussian noise (AWGN)
The standard model of amplifier noise is additive, Gaussian, independent at each pixel and independent of the signal intensity, caused primarily by JohnsonNyquist noise (thermal noise). In color cameras where more amplification is used in the blue color channel than in the green or red channel, there can be more noise in the blue channel.
Amplifier noise is a major part of the "read noise" of an image sensor, that is, of the constant noise level in dark areas of the image.
Median Filter
Median Filter is able to perform some kind of noise reduction on an image or signal. The median filter is a nonlinear digital filtering technique, often used to remove noise. Such noise reduction is a typical preprocessing step to improve the results of later processing.
The median is calculated by first sorting all the pixel values from the surrounding neighbourhood into numerical order and then replacing the pixel being considered with the middle pixel value.
Figure 11: Median Filer
Results
Figure 12 shows original image of BabyGrow
Figure 12: Original Image
Figure 13 shows reconstructed image using Inverse discrete wavelet transform (idwt)
Figure 13: Reconstructed image using Inverse discrete wavelets transform
Figure 14 shows reconstructed image using Median Filter
Figure 14: Reconstructed image using Median Filter
Figure 15 shows Bit Error Rate (BER) performance of PSK channel for image. It has been observed that with increase in SNR values BER values decreases.
Figure 15: BER performance of PSK channel for Image
Figure 16 shows Root Mean Square Error (RMSE) performance of PSK channel for image using WT and Median Filter. It has been observed that with increase in SNR values RMSE values decreases.
Figure 16: RMSE performance of PSK channel for Image
Figure 17 shows Peak Signal to Noise Ratio (PSNR) performance of PSK channel for image using WT and Median Filter. It has been observed that with increase in SNR values PSNR values increases
.
Figure 17: PSNR performance of PSK channel for Image
snr 
ber 
rmse 
psnr 
rmse_wt 
psnr_wt 
rmse_med 
psnr_med 
10 
0.324242 
11.30723 
27.09767 
12.46605 
26.25022302 
11.86370141 
26.68039515 
9 
0.311622 
11.02373 
27.31823 
12.3093 
26.36013234 
11.28133375 
27.11759035 
8 
0.286797 
10.85711 
27.45051 
12.32457 
26.34936537 
11.34313845 
27.07013465 
7 
0.258922 
10.6523 
27.61593 
12.29911 
26.36732517 
11.06008335 
27.28963131 
6 
0.237565 
10.38999 
27.8325 
12.07816 
26.52478143 
10.59205212 
27.66519713 
5 
0.213526 
9.94915 
28.20908 
11.71695 
26.78850572 
9.896001374 
28.25560437 
4 
0.179872 
9.508599 
28.60247 
11.71162 
26.79246178 
9.172149606 
28.91537671 
3 
0.157637 
8.873265 
29.20313 
11.3389 
27.07338138 
7.965207256 
30.14085769 
2 
0.130917 
8.303908 
29.77915 
10.87964 
27.43251146 
6.924438969 
31.35710747 
1 
0.103412 
7.50456 
30.65829 
10.35241 
27.86397228 
5.655710054 
33.11505657 
0 
0.079096 
6.773928 
31.54799 
9.826453 
28.31686399 
4.982254011 
34.216282 
1 
0.05649 
5.878611 
32.77931 
8.997514 
29.08234904 
4.08593887 
35.93896201 
2 
0.038184 
4.659128 
34.79871 
7.030102 
31.2255665 
3.113900406 
38.29870494 
3 
0.023206 
3.6337 
36.95782 
5.205645 
33.83530791 
2.497483941 
40.21474522 
4 
0.013082 
2.938535 
38.80218 
4.659763 
34.79752346 
2.458682237 
40.35075123 
5 
0.006287 
2.10012 
41.71992 
5.555463 
33.2703946 
2.141016045 
41.55240087 
5 
0.005594 
1.923462 
42.48313 
5.470131 
33.40484417 
2.13686645 
41.5692517 
5 
0.005131 
1.441025 
44.99137 
5.301313 
33.67713028 
4.431305056 
35.23416634 
Table 1: SNR , BER, RMSE and PSNR performance of PSK channel for Image using Wavelet Transform and Median Filter
Conclusion
Table 1 shows the performance of PSK channel for image using WT and Median Filter. It has been observed that with increase in SNR values BER values decreases, RMSE values also decreases and PSNR values increases. Image has been more denoised and reconstructed using Median Filter as compare to Wavelet transform.
References

Reeta Charde, Study of Image Reconstruction and Denoising using Wavelet transform ,1st National Conference in BM college Indore ,27th April 2012

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