### Table 4.8: ML Mixed Gaussian Parameter Estimates and RMS Error in Amplitude Dual Tree Complex Wavelet Analysis for Log Transformed Images

in Speckle Noise Reduction via Homomorphic Elliptical Threshold Rotations in the Complex Wavelet Domain

### Table 3. Comparison of two feature extraction methods. Gabor Transform Wavelet Transform

2001

"... In PAGE 6: ... A. Feature Extraction Method Table3 shows the recognition rate on two different feature extraction methods, Gabor transform and Haar wavelet trans- form, with the same classifier. The recognition rate of wavelet transform is better than that of Gabor transform by 0.... ..."

Cited by 21

### Table 5: Comparison with wavelet-based methods

"... In PAGE 21: ...he feature extractions can be seen in Subsection 4.2. In order to show more comparability, all the methods use CLDA and the NN classifier with the Euclidean distance. Table5 shows that the LDC based feature extraction has the best result on the ORL database, both data sets of the FERET database, and it outperforms WaveletFace, though it underperforms LDB and MLDB marginally on the CMU-lights database. Moreover, LDC is more efficient than LDB, MLDB because of the lower computational complexity when K is large, especially on the large FERET data set (K = 255).... In PAGE 22: ... The results on the ORL database, both data sets of the FERET database and the CMU-lights database are shown in Table 6. Comparing the results on Table 6 with Table5 which uses the Euclidean distance, it shows that the triangle square ratio criterion performs better than the Euclidean distance considerably on both data sets of the FERET database and the CMU-lights database, while its efficacy is very close to the Euclidean distance on the ORL database. In fact, the FERET database, the CMU-lights database concern about illumination variations (light intensity and direction respectively), and the ORL database concerns about expression and pose changes.... ..."

### Table 1 Comparison of signal feature extraction among HHT, wavelet, and fourier spectral analyses.

2003

"... In PAGE 7: ...provide additional information even in cases when the structural behavior is nonlinear and non-stationary. Table1 highlights some of the differences of these methods. An alternative approach for structural health monitoring that does not use modal properties is to represent the dynamic response of a structure in terms of the superposition of traveling waves that can traverse individual elements of a struc- ture, reflecting off boundaries to establish stand- ing waves from constructive interferences.... ..."

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### Table 2: Features that influence hospital mortality according to CART and stepwise logistic regression analysis

1996

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### Table 3: Percent energy and coe cients (in parentheses) retained for selected thresholding methods and basis functions de ned as: (i) DAUB #n: The standard Daubechies wavelet basis, (Daubechies, 1988, 1992), DAUB#2 is the HAAR basis; (ii) SDAUB#n: The least asymmetric Daubechies wavelet basis, (Daubechies, 1992); (iii) COIF#n Coi ets, a wavelet basis in which the scaling function has vanishing moments, in addition to the wavelet function; (iv) BSPL#m.n Biorthogonal spline bases based on simple polynomial spline functions of degree m and n for and (Chui, 1992); (v) VSPL A variation on BSPL designed to achieve near-orthogonality; (vi) PACKD#n, wavelet packets based on DAUB #n lters. The WALSH basis is a wavelet packet based on the HAAR lter.

"... In PAGE 7: ... This motivated us to consider two elements in the wavelet thresholding process: the choice of the criterion and the choice of the wavelet basis. Table3 presents... In PAGE 8: ... (1994 a,b) to the in nitely supported spline wavelets used by Yamada and Ohkitani (1990) and Meneveau (1991). Notice in Table3 that the energy conservation and compression ratios are robust to the choice of wavelet bases but not with respect to the choice of wavelet thresholding method. It should be noted in Table 3 that the Universal method resulted in a lower energy loss at the expense of a lower compression ratio when compared to the Lorentz threshold function for all atmospheric stability conditions.... In PAGE 8: ... Notice in Table 3 that the energy conservation and compression ratios are robust to the choice of wavelet bases but not with respect to the choice of wavelet thresholding method. It should be noted in Table3 that the Universal method resulted in a lower energy loss at the expense of a lower compression ratio when compared to the Lorentz threshold function for all atmospheric stability conditions. How- ever, the energy losses due to the Lorentz threshold are well within measurement variance uncertainty (see e.... In PAGE 8: ...41 power-laws. These two approaches are considered next. 4.2 Heat and Momentum Flux Conservation While Table3 demonstrates that all thresholding models are able to concentrate much of the turbulent energy in few coe cients, little is known whether these limited coe cients can reproduce covariances between turbulent variables. That is, the thresholding methodology extracts low-dimensional organized perturba- tions (U(o); W(o); T(o) a ) from velocity (U; W) and temperature (Ta) time series measurements, given by U = U(o) + U(r) W = W(o) + W(r) Ta = T(o) a + T(r) a and lters out the high-dimensional part (U(r); W(r); T(r) a ): As a graphical illus- tration, Figure 2 compares the original (U) and the thresholded (U(o)) longitu- dinal velocity time series for all thresholding methods.... In PAGE 9: ... For this purpose, the momentum and heat uxes using the measured (N = 65; 536), Fourier, Universal, and Lorentz thresholded time series are compared for all 8 runs in Table 4. The Haar and v- spline bases are used as illustration since they represent the extremes in energy conservation and percent coe cients thresholded as evidenced in Table3 . The calculations in Table 4 are performed by thresholding and reconstructing each time series using the non-zero Fourier, wavelet or wavelet packet coe cients.... ..."

### Table 6: Discrete Fourier transform vs. wavelet-packet transform for spare representation example

"... In PAGE 16: ... To motivate the choice of wavelet over Fourier consider the function f(x1; x2) = b0 + b1x1 + b2x2 + b3x1x2, and the associated samples show in Table 5. If we perform a discrete (trigonomic) Fourier and a wavelet-packet transform on the data, we obtain the results presented in Table6 . The wavelet transform is seen to provide a sparser representation of the feature variables, re ecting the orthogonal basis in the feature space.... ..."

### Table 2 Classification rate of FFT and wavelet features FFT (k = 4) Wavelet (k = 11)

"... In PAGE 7: ... We compared the classification performance of wavelet based feature extraction method with the FFT based method described in [20] by using the weighted k-NN rule. The classification rate of each experiment is shown in Table2 . The last line in Table 2 is the classification rate which is the ratio of the sum of correct classified samples and testing samples of the 7 experiments.... In PAGE 7: ... Table2 shows that FFT feature has high classification rate of some testing sets while some others are very low. The classification rate of AAV 3 is seriously wrong.... ..."

### Table 1. A summary of the principal families of approaches and related principles, properties and functionalities.

2005

"... In PAGE 6: ... section 3). Table1 summarizes the principles, properties, and offered functionalities of the different families of approaches. ... In PAGE 7: ... Our evaluation is based on the computation times reported in the literature. Table1 shows that only the wavelet-based techniques provide both progressive transmission and scalable rendering. In particular, the irregular wavelet transform has a very low computational complexity, which makes it very attractive for mobile and real-time applications.... ..."

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