WavBox 4: A Software Toolbox for Wavelet Transforms and Adaptive Wavelet Packet Decompositions

Author(s):  
Carl Taswell
2018 ◽  
Vol 66 (7) ◽  
pp. 2947-2957 ◽  
Author(s):  
Marwa Chafii ◽  
Jacques Palicot ◽  
Remi Gribonval ◽  
Faouzi Bader

Author(s):  
Chi-Man Pun

It is well known that the sensitivity to translations and orientations is a major drawback in 2D discrete wavelet transform (DWT). In this paper, we have proposed an effective scheme for rotation invariant adaptive wavelet packet transform. During decomposition, the wavelet coefficients are obtained by applying a polar transform (PT) followed by a row-shift invariant wavelet packet decomposition (RSIWPD). In the first stage, the polar transform generates a row-shifted image and is adaptive to the image size to achieve complete and minimum sampling rate. In the second stage, the RSIWPD is applied to the row-shifted image to generate rotation invariant but over completed subbands of wavelet coefficients. In order to reduce the redundancy and computational complexity, we adaptively select some subbands to decompose and form a best basis representation with minimal information cost with respect to an appropriate information cost function. With this best basis representation, the original image can be reconstructed easily by applying a row-shift invariant wavelet packet reconstruction (RSIWPR) followed by an inverse polar transform (IPT). In the experiments, we study the application of this representation for texture classification and achieve 96.5% classification accuracy.


2013 ◽  
Vol 39 (12) ◽  
pp. 2463-2476 ◽  
Author(s):  
Sankaralingam Esakkirajan ◽  
Chinna Thambi Vimalraj ◽  
Rashad Muhammed ◽  
Ganapathi Subramanian

2016 ◽  
Vol 15 (1) ◽  
pp. 67
Author(s):  
M. L. S. Indrusiak ◽  
A. J. Kozakevicius ◽  
S. V. Möller

In this work, wavelet transforms are the analysis tools for studying transient and discontinuous phenomena associated to turbulent flows. The application in quest results from velocity measurements with hot wire anemometry in the transient wake considering a circular cylinder in an aerodynamic channel. Continuous and discrete wavelet transforms are applied and compared with the corresponding results given by the Fourier transform. For the continuous wavelet transform, the Morlet function was adopted as transform basis, and for the discrete case, the Daubechies orthonormal wavelet with 20 null moments. Results using the discrete wavelet packet transform are also presented and compared. A wake past a cylinder was analytically simulated and compared with the actual one, both in transient flow. The ability of the wavelet transforms in the analysis of unsteady phenomena and the potential of the wavelet approach as a complementary tool to the Fourier spectrum for the analysis of stationary phenomena is presented and discussed.


Author(s):  
N Li ◽  
C Liu ◽  
C He ◽  
Y Li ◽  
X F Zha

In this article, a novel fault detection method based on adaptive wavelet packet feature extraction and relevance vector machine (RVM) is proposed for incipient fault detection of gear. First, ten statistical characteristics in time domain and all node energies of full wavelet packet tree are extracted as candidate features. Then, Fisher criterion is applied to evaluate the discrimination power of each feature. Finally, two optimal features from time domain and wavelet domain, respectively, are selected to be used as inputs to the RVM. Furthermore, moving average is applied to each feature to improve accuracy for online continuous fault detection. By combining wavelet packet transform with Fisher criterion, it is able to adaptively find the optimal decomposition level and select the global optimal features. The RVM, a Bayesian learning framework of statistical pattern recognition, is adopted to train the fault detection model. The RVM was compared with the popular support vector machine (SVM) with the increase of training samples. Experimental results validate the effectiveness of the proposed method, and indicate that RVM is more suitable than SVM for online fault detection.


1996 ◽  
Author(s):  
Ryan Benton ◽  
Afshin Ganjoo ◽  
Beth Lumetta ◽  
Daryl Spillman ◽  
Jason Ring

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