Selection of Optimal Decomposition Layer for Thresholding Denoising Using Singular Spectrum Analysis and Wavelet Entropy

Zhi Cui,Xian-pu Cui 보안공학연구지원센터 2016 International Journal of Multimedia and Ubiquitous Vol.11 No.4

To optimize the number of decomposition layers in wavelet threshold denoising for ultrasonic signals, we propose a self-adaptive algorithm of determining the number of decomposition layers based on singular spectrum analysis and wavelet entropy. First the noise-containing signals are decomposed by discrete wavelet transform. The slope of the singular value spectrum for each layer is estimated. Then the wavelet entropy over the signal subinterval is calculated for each layer. Finally the optimal number of decomposition layer is determined by combining the entropy ratio of detail coefficients to original signal and the slope of the singular value spectrum. The performance of the algorithm is evaluated using signal-to-noise ratio (SNR) and the relative error of the peak value (REPV). Experiment shows that the algorithm can self-adaptively determine the optimal number of decomposition layers and filter out the noise contained in the ultrasonic signals. It not only increases the SNR, but also preserves valuable components of the original signal.

Crack identification with parametric optimization of entropy & wavelet transformation

Wimarshana, Buddhi,Wu, Nan,Wu, Christine Techno-Press 2017 Structural monitoring and maintenance Vol.4 No.1

A cantilever beam with a breathing crack is studied to improve the breathing crack identification sensitivity by the parametric optimization of sample entropy and wavelet transformation. Crack breathing is a special bi-linear phenomenon experienced by fatigue cracks which are under dynamic loadings. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a fatigue crack. To improve the sensitivity of entropy measurement for crack identification, wavelet transformation is merged with entropy. The crack identification is studied under different sinusoidal excitation frequencies of the cantilever beam. It is found that, for the excitation frequencies close to the first modal frequency of the beam structure, the method is capable of detecting only 22% of the crack depth percentage ratio with respect to the thickness of the beam. Using parametric optimization of sample entropy and wavelet transformation, this crack identification sensitivity is improved up to 8%. The experimental studies are carried out, and experimental results successfully validate the numerical parametric optimization process.

Optimization-based Image Watermarking Algorithm Using a Maximum-Likelihood Decoding Scheme in the Complex Wavelet Domain

( Jinhua Liu ),( Yunbo Rao ) 한국인터넷정보학회 2019 KSII Transactions on Internet and Information Syst Vol.13 No.1

Most existing wavelet-based multiplicative watermarking methods are affected by geometric attacks to a certain extent. A serious limitation of wavelet-based multiplicative watermarking is its sensitivity to rotation, scaling, and translation. In this study, we propose an image watermarking method by using dual-tree complex wavelet transform with a multi-objective optimization approach. We embed the watermark information into an image region with a high entropy value via a multiplicative strategy. The major contribution of this work is that the trade-off between imperceptibility and robustness is simply solved by using the multi-objective optimization approach, which applies the watermark error probability and an image quality metric to establish a multi-objective optimization function. In this manner, the optimal embedding factor obtained by solving the multi-objective function effectively controls watermark strength. For watermark decoding, we adopt a maximum likelihood decision criterion. Finally, we evaluate the performance of the proposed method by conducting simulations on benchmark test images. Experiment results demonstrate the imperceptibility of the proposed method and its robustness against various attacks, including additive white Gaussian noise, JPEG compression, scaling, rotation, and combined attacks.

A Partial Discharge Fault Identification Algorithm based on SGWT Neural Network

Wei Zhang,Qiuli Wu,Yurong Deng 보안공학연구지원센터 2016 International Journal of Grid and Distributed Comp Vol.9 No.5

Based on the second generation wavelet and information entropy, in this paper, we recognize the partial discharge pattern using the second generation wavelet (SGWT) and adaptive BP. Firstly, feature extraction of discharge signals are obtained using the SGWT and information entropy. Then, the extracted features are feed into the training BP network. The learning algorithm employed the conjugate gradient methods and the adaptive adjustment to train the error for BP network. Finally, we get the optimum training network, and the simulation results verified the feasibility of the algorithm.

Improving Lookup Time Complexity of Compressed Suffix Arrays using Multi-ary Wavelet Tree

Wu, Zheng,Na, Joong-Chae,Kim, Min-Hwan,Kim, Dong-Kyue Korean Institute of Information Scientists and Eng 2009 Journal of Computing Science and Engineering Vol.3 No.1

In a given text T of size n, we need to search for the information that we are interested. In order to support fast searching, an index must be constructed by preprocessing the text. Suffix array is a kind of index data structure. The compressed suffix array (CSA) is one of the compressed indices based on the regularity of the suffix array, and can be compressed to the $k^{th}$ order empirical entropy. In this paper we improve the lookup time complexity of the compressed suffix array by using the multi-ary wavelet tree at the cost of more space. In our implementation, the lookup time complexity of the compressed suffix array is O(${\log}_{\sigma}^{\varepsilon/(1-{\varepsilon})}\;n\;{\log}_r\;\sigma$), and the space of the compressed suffix array is ${\varepsilon}^{-1}\;nH_k(T)+O(n\;{\log}\;{\log}\;n/{\log}^{\varepsilon}_{\sigma}\;n)$ bits, where a is the size of alphabet, $H_k$ is the kth order empirical entropy r is the branching factor of the multi-ary wavelet tree such that $2{\leq}r{\leq}\sqrt{n}$ and $r{\leq}O({\log}^{1-{\varepsilon}}_{\sigma}\;n)$ and 0 < $\varepsilon$ < 1/2 is a constant.

Complexity Comparison for Drinkers' and Normal People's EEG Using Wavelet Entropy

Jiufu Liu,Lei Gao,Zaihong Zhou,Haiyang Liu,Zhengqian Wang,Wenyuan Liu,Jianyong Zhou 보안공학연구지원센터 2015 International Journal of Hybrid Information Techno Vol.8 No.8

This paper investigates the influence of alcohol on brain complexity. Considering electro-encephalogram (EEG) has the nonlinear dynamics characteristic of time-varying and non-stationary, we introduce the wavelet entropy (WE) analysis. We denoise EEG signal by using wavelet decomposition, then calculate the wavelet entropy of the denoised signal and analyze the nonlinear complexity. In 64 conductive poles experiments and in different stimulus experiments for FP2 electrode's EEG, the drinkers' EEG wavelet entropy is greater than normal people's. The wavelet entropy of every conductive pole of drinkers’ or normal persons’ is inconformity.

Ultrasonic Signal De-noising Based on Wavelet Entropy and Inter-Scale Correlation

Zhi Cui,Xianpu Cui 보안공학연구지원센터 2016 International Journal of Multimedia and Ubiquitous Vol.11 No.1

In this paper, we proposed an adaptive threshold de-noising method by combining wavelet entropy and inter-scale correlation. Different from the traditional wavelet threshold based de-noising methods, our method can be divided into three steps. First, we decompose the noisy signal by using discrete wavelet transform (DWT), calculate the value of inter-scale correlation of the decomposed wavelet coefficients, and delete the high frequency coefficients which are smaller than the value of inter-scale correlation. Secondly, we equally divide the processed high frequency coefficients into several subintervals, calculate the wavelet entropy of each subinterval, and decide the threshold of high frequency coefficients by combining wavelet entropy and adaptive threshold rules. Finally, we de-noise the high frequency coefficients by using logarithmic smoothing threshold function, and reconstruct the ultrasonic signal. Experiment results have shown that the proposed method is better than some other de-noising methods in terms of SNR (signal noise ratio) and SDR (signal distortion ration).

Research on a Signal Analysis Method based on Wavelet Theory and Approximate Entropy Algorithm

Xiaoyong Yu 보안공학연구지원센터 2016 International Journal of Future Generation Communi Vol.9 No.8

The vibration signal is one of the significant signals that reflects the fault. In allusion to the shortcomings of traditional signal analysis method in the high-frequency and non-stationary signal analysis, the wavelet theory and approximate entropy algorithm are introduced into the signal analysis in order to propose a new vibration signal analysis (WTAEAVSA) method in this paper. In the proposed WTAEAVSA method, the wavelet transform technology is used to reduce the noise and decompose the low and high frequency vibration signal in order to obtain the signal characteristics of different frequency bands. Then the approximate entropy algorithm is used to determine the complexity and irregular degree of vibration signal in the different scale and different frequency band, so as the non-stationary characteristics of vibration signal are extracted. At last, some simulated signals with time-domain and frequency-domain from the normal signal are used to test the characteristics of the proposed WTAEAVSA method. The simulation results show that the proposed WTAEAVSA method can extract the characteristic vector from vibration signal, visually and sharply reflect the changes of the mechanical states.

공간-주파수 적응적 영상복원을 위한 Vaguelette-Wavelet 분석 기술

전신영(Sinyoung Jun),이은성(Eunsung Lee),김상진(Sangjin Kim),백준기(Joonki Paik) 大韓電子工學會 2009 電子工學會論文誌-SP (Signal processing) Vol.46 No.6

본 논문에서는 베이글릿-웨이블릿 분석(vaguelette-wavelet decomposition; VWD)을 이용한 공간-주파수 적응적 영상복원 알고리듬을 제안한다. 제안한 알고리듬은 웨이블릿 계수의 공간적 정보를 이용하여 평탄 영역과 에지 영역을 분리하고, 적응적 웨이블릿 계수축소(wavelet shrinkage)를 통해 잡음 성분을 억제한다. 뿐만 아니라, 에지 영역에서는 엔트로피(entropy)를 적용하여 웨이블릿 부대역의 잡음 성분을 추정하고, 부대역 간의 상관관계를 이용하여 잡음 성분을 억제한다. 이렇게 억제된 웨이블릿 계수의 베이글릿 역변환을 통해 영상을 복원 할 수 있다. 제안한 알고리듬에 사용되는 베이글릿 함수는 잡음을 추정 및 억제 할 수 있을 뿐만 아니라 세밀한 에지 성분의 보존이 가능하도록 변형을 한다. 실험결과에서는 제안한 알고리듬이 잡음에 강건하고, 세밀한 에지 성분을 보전하면서 효과적으로 열화된 영상을 복원할 수 있음을 보여준다. In this paper, we present a novel space-frequency adaptive image restoration approach using vaguelette-wavelet decomposition (VWD). The proposed algorithm classifies a degraded image into flat and edge regions by using spatial information of the wavelet coefficient. For reducing the noise we perform an adaptive wavelet shrinkage process. At edge region candidates, we adopt entropy approach for estimating the noise and remove it by using relative between sub-bands. After shrinking wavelet coefficients process, we restore the degraded image using the VWD. The proposed algorithm can reduce the noise without affecting the sharpness details. Based on the experimental results, the proposed algorithm efficiently proved to be able to restore the degraded image while preserving details.

엔트로피 가중치와 웨버 법칙을 이용한 세일리언시 검출

이호상(Ho Sang Lee),문상환(Sang Whan Moon),엄일규(Il Kyu Eom) 대한전자공학회 2017 전자공학회논문지 Vol.54 No.1