Kalavathy Sundarrajan and Ramalingam M. Suresh
Discrete wavelet transform, ´a trous algorithm, denoising, neighbour-hood pixel difference (NPD)
Image denoising using the wavelet transform has been attracting much attention. Image corrupted by a noise is a classical problem in the field of signal or image processing. `A Trous algorithm is intro- duced to overcome the problem of translation variant mechanism, existing on using discrete wavelet transform (DWT). This algorithm up samples low-pass filter by inserting zeros between the filter co- efficients at each level and accordingly the low-pass and high-pass filter coefficients are modified. The efficiency of wavelet images by using this algorithm is low because the detail preservations of images at different scales are not uniform; also random noise rapidly attenuates with increasing scales. Due to this the contrast of the resulting image is weaker. In order to improve the clarity of the image an algorithm called a neighbourhood pixel filtering algorithm (NPFA) is added along with the existing `a trous algorithm. In the proposed algorithm, find neighbourhood pixel difference (NPD) by subtracting the neighbourhood pixel values from its current noisy pixel value. Also, calculate weight of each pixel which depends on this NPD. A filtered value is assigned for each current pixel in order to approximate the original pixel value of that pixel. This filtered value is generated by minimizing NPD and weighted mean square error (WMSE) using method of least square. A reduction in noise pixel is observed on replacing the optimal weight namely NPFA filter solution with the noisy value of the current pixel. Due to this NPFA filter gain the effect of both high-pass and low-pass filter. This filter behaves like a low-pass filter in smooth region by decreasing noise variance effectively and giving similar weights to all its neighbourhood pixels. This in turn cuts off only high frequency noise signal instead of all noisy signals. The resultant image thus obtained is observed to have much less blurring effect compared to the other wavelet method. ∗ Research Scholar, Dr. M.G.R. Educational and Research Institute – University, Maduravoyal, Chennai; Department of Mathematics, R.M.D. Engineering College, Kavaraipettai 601 206, India; e-mail: [email protected] ∗∗ Department of Computer Science and Engineering, R.M.D. Engineering College, Kavaraipettai 601 206, India; e-mail: [email protected] Recommended by Dr. J. Shen
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