A Wavelet Packet Tree Denoising Algorithm for Images of Atomic-Force Microscopy
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In: Asian Journal of Control, Vol. 20, No. 4, 07.2018, p. 1367-1378.
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - A Wavelet Packet Tree Denoising Algorithm for Images of Atomic-Force Microscopy
AU - Schimmack, Manuel
AU - Mercorelli, Paolo
PY - 2018/7
Y1 - 2018/7
N2 - A threshold-free denoising procedure of acquired discrete Atomic-force microscopy (AFM) signals using the discrete wavelet transform (DWT) method is presented in this article. The integration of a denoising procedure into a control structure is extremely important for each kind of system to be controlled. The detection of unavoidable measurement noise in the acquired data of the AFM signal is done by using orthogonal wavelets (Daubechies and Symmlet) and with different polynomial approximation order for each family. The proposed denoising algorithm, based on the free wavelet toolboxes from the WaveLab 850 library of the Stanford University (USA), compares the usefulness of Daubechies and Symmlet wavelets with different vanishing moments. With the help of a seminorm the noise of a sequence is defined as a coherent and incoherent part of the AFM signal. In the first step of the procedure the algorithm analyzes the frequency subspaces of the wavelet packets tree and searches for small or opposing components in the wavelet domains. In the second step of the procedure the incoherent components in the low- and high frequency domains are localized and the incoherent is then removed from the AFM signal. The proposed algorithm structure is used to improve the quality of the AFM signals and it can be easily integrated into the existing AFM control hard- and software structures. The effectiveness of the proposed denoising algorithm is validated with real measurements.
AB - A threshold-free denoising procedure of acquired discrete Atomic-force microscopy (AFM) signals using the discrete wavelet transform (DWT) method is presented in this article. The integration of a denoising procedure into a control structure is extremely important for each kind of system to be controlled. The detection of unavoidable measurement noise in the acquired data of the AFM signal is done by using orthogonal wavelets (Daubechies and Symmlet) and with different polynomial approximation order for each family. The proposed denoising algorithm, based on the free wavelet toolboxes from the WaveLab 850 library of the Stanford University (USA), compares the usefulness of Daubechies and Symmlet wavelets with different vanishing moments. With the help of a seminorm the noise of a sequence is defined as a coherent and incoherent part of the AFM signal. In the first step of the procedure the algorithm analyzes the frequency subspaces of the wavelet packets tree and searches for small or opposing components in the wavelet domains. In the second step of the procedure the incoherent components in the low- and high frequency domains are localized and the incoherent is then removed from the AFM signal. The proposed algorithm structure is used to improve the quality of the AFM signals and it can be easily integrated into the existing AFM control hard- and software structures. The effectiveness of the proposed denoising algorithm is validated with real measurements.
KW - Atomic-force microscopy
KW - Denoising algorithm
KW - Orthogonal wavelets
KW - Wavelet packets transform method
KW - Engineering
UR - http://www.scopus.com/inward/record.url?scp=85040168585&partnerID=8YFLogxK
U2 - 10.1002/asjc.1718
DO - 10.1002/asjc.1718
M3 - Journal articles
AN - SCOPUS:85040168585
VL - 20
SP - 1367
EP - 1378
JO - Asian Journal of Control
JF - Asian Journal of Control
SN - 1561-8625
IS - 4
ER -