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: kalavathysundar@gmail.com ∗∗ Department of Computer Science and Engineering, R.M.D. Engineering College, Kavaraipettai 601 206, India; e-mail: rmsuresh@hotmail.com Recommended by Dr. J. Shen

Important Links:

Go Back