A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing

• Yingxu Zhang,
• Yingzi Li,
• Zihang Song,
• Zhenyu Wang,
• Jianqiang Qian and
• Junen Yao

Beilstein J. Nanotechnol. 2019, 10, 2346–2356, doi:10.3762/bjnano.10.225

• “unsupervised destripe” to remove the non-uniform stripe noises from AFM images. Orthogonal wavelets are applied to filter the Gaussian noise from AFM images [6]. For the impulse noise in AFM images, the median filter is generally applied [7][8], where every pixel is replaced by the median value of pixels of

Graphene–polymer coating for the realization of strain sensors

• Carmela Bonavolontà,
• Carla Aramo,
• Massimo Valentino,
• Giampiero Pepe,
• Sergio De Nicola,
• Gianfranco Carotenuto,
• Angela Longo,
• Mariano Palomba,
• Simone Boccardi and
• Carosena Meola

Beilstein J. Nanotechnol. 2017, 8, 21–27, doi:10.3762/bjnano.8.3

• the data with the spectrum acquired on the bare substrate using a numerical data treatment based on a wavelets algorithm and linear regression [19]. The relative variation of electrical resistance ΔR/R0 is plotted as a function of the applied strain ε (Figure 9), where the data refer to two sets of

Near-field visualization of plasmonic lenses: an overall analysis of characterization errors

• Jing Wang,
• Yongqi Fu,
• Zongwei Xu and
• Fengzhou Fang

Beilstein J. Nanotechnol. 2015, 6, 2069–2077, doi:10.3762/bjnano.6.211

• free space. The perforated elliptical slits are adopted here for the purpose of controlling the focused region from both x- and y-directions. The focal region is formed by the SPPs-enhanced interference of the diffraction wavelets originating from the slits [5][13]. Figure 2 shows the calculated

Can molecular projected density of states (PDOS) be systematically used in electronic conductance analysis?

• Tonatiuh Rangel,
• Gian-Marco Rignanese and
• Valerio Olevano

Beilstein J. Nanotechnol. 2015, 6, 1247–1259, doi:10.3762/bjnano.6.128

• Method 2, an interpretation which depends on the chosen basis set (e.g., WFs, LCAO, Gaussians or wavelets) cannot be considered physical. We believe that a completely different direction should be taken in order to provide an answer to these questions. What matters for a physical interpretation of the

Energy dissipation in multifrequency atomic force microscopy

• Valentina Pukhova,
• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2014, 5, 494–500, doi:10.3762/bjnano.5.57

• our previous work [5]. Wavelet analysis allows to follow the spectral content of a signal h(t) that evolves in time by projecting (convoluting) the signal over a set of oscillating functions with zero mean and a limited support (wavelets) that are obtained by the translations (or delays, d) and

• dilations (or scaling, s) of a mother wavelet Ψ(t) [7]. The temporal convolution of the signal with the wavelets at all possible scales and delays constitute the wavelet transform (WT) of the signal Wh(s,d) [7]. Scaling is connected to frequency, delays to time. The signal spectrum Wh(s,d) is a frequency

• –time representation that gives a measure of the local, i.e., at the point (s,d), resemblance of the signal and the wavelet. In wavelet analysis the basis can be chosen among an infinite set of functions that are mathematically admissible, in this work we use the complex Gabor wavelets [8][9]. To cross

Wavelet cross-correlation and phase analysis of a free cantilever subjected to band excitation

• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2012, 3, 294–300, doi:10.3762/bjnano.3.33

• oscillating function, and rapid decay at infinity (technically Ψ(t) must be continuous and have a compact support; this is called the admissibility condition), are called wavelets. The convolution of f(t) with Ψs,d(t), at the scale s and delay d, is the wavelet transform (WT) of the signal Wf(s,d): This is a

Extended X-ray absorption fine structure of bimetallic nanoparticles

• Carolin Antoniak

Beilstein J. Nanotechnol. 2011, 2, 237–251, doi:10.3762/bjnano.2.28

• density functional theory calculations on the magnetic properties. Keywords: bimetallic alloys; EXAFS; FePt; nanoparticles; wavelets; XAS; Introduction Since the discovery of X-rays in 1895 by Röntgen, the field of spectroscopy methods using this regime of the electromagnetic spectrum has reached a very

• resolution in k, but the cutting has to be performed carefully so as not to lose good resolution in Fourier space. The most recent solution up to now is the wavelet transform (WT). WTs gained much attention in the 1990s after the discovery of a family of orthogonal continuous wavelets by Daubechies [64

• ]. Wavelets are square-integrable functions and the integral over the wavelet is zero: Today wavelets are widely used to extract information from audio signals and images, and for compression/decompression algorithms. However, in EXAFS analysis they are only used occasionally [65][66][67][68][69]. The main

Tip-sample interactions on graphite studied using the wavelet transform

• Giovanna Malegori and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2010, 1, 172–181, doi:10.3762/bjnano.1.21

• , i.e., signal with a frequency spectrum changing during the data collection. This work will show that the tip-sample interaction forces can be quantitatively measured using CWT with acquisition times as short as few tens of milliseconds, as required for practical DFS imaging. Since wavelets are a

• oscillating function. The function Ψ(t) is called a mother wavelet, the translated and dilated replicas Ψs,d(t) are called daughter wavelets. The wavelet transform of a function of time t, f(t), at the scale s and delay d is computed by correlating f(t) with the daughter wavelet at the corresponding scale and

• signal at the given delay and scale, called the scalogram of the signal. As explained in detail below, the delay-scale representation in which wavelets are defined can be mapped into the more physical time-frequency representation to describe the signal energy localization in frequency and time. It is