An on-line orthogonal wavelet denoising algorithm for high-resolution surface scans
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In: Journal of the Franklin Institute, Vol. 355, No. 18, 12.2018, p. 9245-9270 .
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - An on-line orthogonal wavelet denoising algorithm for high-resolution surface scans
AU - Schimmack, Manuel
AU - Mercorelli, Paolo
PY - 2018/12
Y1 - 2018/12
N2 - 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).
AB - 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).
KW - Engineering
UR - http://www.scopus.com/inward/record.url?scp=85026630450&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2017.05.042
DO - 10.1016/j.jfranklin.2017.05.042
M3 - Journal articles
AN - SCOPUS:85026630450
VL - 355
SP - 9245
EP - 9270
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
SN - 0016-0032
IS - 18
ER -