The wavelet response as a multiscale NDT method

Ultrasonics ◽  
2003 ◽  
Vol 41 (6) ◽  
pp. 487-497 ◽  
Author(s):  
Y. Le Gonidec ◽  
F. Conil ◽  
D. Gibert
Keyword(s):  
Wavelet Response

Improved SURF Descriptor Based on Triangle Partition

2013 ◽  
Vol 718-720 ◽  
pp. 2296-2301 ◽  
Author(s):  
Zeng Luan ◽  
Zhai You ◽  
Xiong Wei
Keyword(s):  
Real Time ◽  
Image Matching ◽  
Weighting Function ◽  
Boundary Effect ◽  
Haar Wavelet ◽  
Local Region ◽  
Experimental Results ◽  
Time Performance ◽  
Wavelet Response ◽  
Better Than

In order to improve the robustness and real time performance of SURF based image matching algorithms, a new descriptor is proposed. We compute the new descriptor in a rectangle local region (the side set to 20s). Firstly, the local region is divided into 8 equal triangle subregion. Secondly, local region location grid is rotated to align its dominate orientation to a canonical direction. The keypoint dominate orientation and its orthogonalorientation is defined as the x and y directions of the descriptors local coordinate system.Thirdly, compute the Haar wavelet response in x and y directions within the keypoint local region. In order to reduce the boundary effect and outer noise, Haar wavelet response in the same Grid of different triangle is both assigned to each triangle in different weight, and then a gaussian weighting function is used. Compute the histogram of Haar wavelet response and absolute Haar wavelet response, so each triangle subregion constitutes a vector with 4 dimensions. Finally, a descriptor with 32 dimensions is constituted and the descriptor is normalized to achieve illumination invariance. The experimental results show that the performance of the new descriptor is even better than SURF descriptor.

scholarly journals SYMMETRIZATION AND ENHANCEMENT OF THE CONTINUOUS MORLET TRANSFORM FOR SPECTRAL DENSITY ESTIMATION

2012 ◽  
Vol 10 (01) ◽  
pp. 1250009 ◽  
Author(s):  
ROBERT W. JOHNSON
Keyword(s):  
Spectral Density ◽  
Wavelet Spectrum ◽  
Response Matrix ◽  
Spectral Density Estimation ◽  
Spectral Leakage ◽  
Maximum Resolution ◽  
Harmonic Content ◽  
Instant Power ◽  
The Mean ◽  
Wavelet Response

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet power and the integrated instant power, giving a quantitative estimate of the power density with temporal resolution. Deconvolution with the wavelet response matrix reduces the spectral leakage and produces an enhanced wavelet spectrum providing maximum resolution of the harmonic content of a signal. Applications to data analysis are discussed.

scholarly journals The wavelet response as a multiscale characterization of scattering processes at granular interfaces

Ultrasonics ◽  
2006 ◽  
Vol 44 (4) ◽  
pp. 381-390 ◽  
Author(s):  
Yves Le Gonidec ◽  
Dominique Gibert
Keyword(s):  
Wavelet Response

The effect of topography on the wavelet response of seismic arrays

1994 ◽  
Author(s):  
Abdullatif A. Al‐Shuhail ◽  
Anthony F. Gangi
Keyword(s):  
Seismic Arrays ◽  
Wavelet Response

scholarly journals Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes

2018 ◽  
Vol 6 (3) ◽  
pp. 76
Author(s):  
Somayeh Kokabisaghi ◽  
Eric Pauwels ◽  
Katrien Van Meulder ◽  
André Dorsman
Keyword(s):  
Time Series ◽  
Sensitivity Analysis ◽  
Parameter Estimates ◽  
Financial Assets ◽  
Attraction Force ◽  
Stochastic Behaviour ◽  
Central Value ◽  
Wavelet Response ◽  
Random Fluctuations ◽  
Mean Reverting Process

The CKLS process (introduced by Chan, Karolyi, Longstaff, and Sanders) is a typical example of a mean-reverting process. It combines random fluctuations with an elastic attraction force that tends to restore the process to a central value. As such, it is widely used to model the stochastic behaviour of various financial assets. However, the calibration of CKLS processes can be problematic, resulting in high levels of uncertainty on the parameter estimates. In this paper we show that it is still possible to draw solid conclusions about certain qualitative aspects of the time series, as the corresponding indicators are relatively insensitive to changes in the CKLS parameters.

Robust deconvolution by modified Wiener filtering

Geophysics ◽  
1988 ◽  
Vol 53 (2) ◽  
pp. 186-191 ◽  
Author(s):  
A. T. Walden
Keyword(s):  
Additive Noise ◽  
Noise Suppression ◽  
Mean Squared Error ◽  
Wiener Filter ◽  
Frequency Function ◽  
A Value ◽  
Squared Error ◽  
Simple Variant ◽  
Wavelet Response ◽  
Frequency Functions

Deconvolution in the presence of additive noise is a well known problem for which there exists a Wiener filter which spectrally whitens while also suppressing the noise. A simple variant of this standard Wiener filter incorporates a parameter p which is intended to allow further weight to be given to noise suppression. This filter is often called a modified Wiener filter. To design such a filter, one must know the frequency characteristics of the wavelet precisely, plus the spectra of the input and additive noise. Typically, some appropriate estimate of the frequency function of the wavelet is taken, and the modified Wiener filter is designed from that estimate. A more realistic practical viewpoint is to think of the estimated wavelet response as one of a set of possible frequency response functions. By using statistical information obtained during wavelet estimation, a value of p can be chosen which gives a modified Wiener filter equivalent to a statistically robust deconvolution filter. Here “robust” means that the error criterion which defines the deconvolution filter allows for the set of possible wavelet frequency functions. Two different error criteria are considered: (1) the minimization of the average mean‐squared error, and (2) the minimization of the maximum mean‐squared error. Deconvolution using an estimated wavelet can thus be made robust to wavelet uncertainties in an easily followed technique.

An autoregressive filter model for constant Q attenuation

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 749-758 ◽  
Author(s):  
Lon A. McCarley
Keyword(s):  
Seismic Waves ◽  
Seismic Wave Propagation ◽  
Good Representation ◽  
Minimum Phase ◽  
Inverse Filter ◽  
Low Frequencies ◽  
Filter Model ◽  
Sonic Log ◽  
Wavelet Response ◽  
Filter Response

The Earth’s filter response to seismic wave propagation can be approximated by constant Q attenuation and is dispersive or minimum phase. A finite‐length autoregressive (AR) filter model is a good representation for constant Q attenuation with minimum phase. Coefficients of the AR filter are the Wiener‐Levinson inverse filter coefficients for the sampled constant Q auto‐correlation. Conventional spike deconvolution approximates fairly well the inverse filter on this ground if the minimum‐phase attenuation law holds true. Wavelet response to attenuation was analyzed using the AR filter model. The amplitude of the filtered impulse response decreases at nearly 1/t, where t is traveltime, and is sensitive to the loss of low frequencies. The wavelets’ peak amplitude is fractionally time delayed with .92/Q. Velocity dispersion of seismic waves should not contribute to the mis‐tie observed between the conventional check shot and the borehole sonic log when the first arrivals are picked the same way.

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