An on-line orthogonal wavelet denoising algorithm for high-resolution surface scans |
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| Institution: | 1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russian Federation;2. Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Russian Federation;3. Vologda State University, Russian Federation;4. Institute of Socio-Economic Development of Territories, RAS, Russian Federation;1. Civil and Environmental Engineering, 413 Durham Hall, MC0246, 1145 Perry Street, Virginia Tech, Blacksburg, VA 24061, USA;2. Chemistry, Hahn Hall South, MC004C, Virginia Tech, Blacksburg, VA 24061, USA;1. Institute of Mathematical Sciences, Department of Mathematics, Chennai 600 113, Tamil Nadu, India;2. S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, West Bengal, India;3. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA |
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| Abstract: | This paper deals with noise detection and threshold free on-line denoising procedure for discrete scanning probe microscopy (SPM) surface images using wavelets. In this sense, the proposed denoising procedure works without thresholds for the localisation of noise, as well for the stop criterium of the algorithm. In particular, a proposition which states a constructive structural property of the wavelets tree with respect to a defined seminorm has been proven for a special technical case. Using orthogonal wavelets, it is possible to obtain an efficient localisation of noise and as a consequence a denoising of the measured signal. An on-line denoising algorithm, which is based upon the discrete wavelet transform (DWT), is proposed to detect unavoidable measured noise in the acquired data. With the help of a seminorm the noise of a signal is defined as an incoherent part of a measured signal and it is possible to rearrange the wavelet basis which can illuminate the differences between its coherent and incoherent part. In effect, the procedure looks for the subspaces consisting of wavelet packets characterised either by small or opposing components in the wavelet domain. Taking real measurements the effectiveness of the proposed denoising algorithm is validated and compared with Gaussian FIR- and Median filter. The proposed method was built using the free wavelet toolboxes from the WaveLab 850 library of the Stanford University (USA). |
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