New Wavelet Theory and Application in Nondestructive Testing

A new ultrasound signal processing model that provides fast real-time performance was developed. The model is based on the “rotation angle series fast wavelet transform“ algorithm developed for realtime digital signal processing. Instead of the traditional convolution-based algorithms, the algorithm uses a cascaded structure which can be quickly implemented on digital signal processors. The algorithm runs twice as fast as and is more flexible than the fast wavelet transform, and is applicable for multi-channel and phased array ultrasound systems. By using this algorithm, multi-channel ultrasound systems, including phased array ultrasound systems can have less complex software and hardware designs, lower cost,smaller size, and especially more powerful functions.     

A quasi-geostrophic wavelet-spectrum model for barotropic atmosphere and its numerical solution

A quasi-geostrophic wavelet-spectrum model of barotropic atmosphere has been constructed by wavelet-Galerkin method with the periodic orthogonal wavelet bases. In this study a wavelet grid-spectrum transform method is designed to decrease the tremendous computation of the nonlinear interaction term in the model, and a two-dimensional Helmholtz equation from the model in a wavelet spectrum form is derived, and a solution with high precision under the periodic boundary condition is obtained. The numerical investigation manifests that the wavelet-spectrum model (WSM) could keep on running for a long time under the forcing of heating and topography. Although its numerical solution is compatible with the grid model (GM), the WSM is of a higher precision and faster convergence rate than GM's. A stationary solution comes forth when the model is forced only by the surface heating, whereas a quasi-periodic oscillation with a period about 15 days appears as considering the topography in the model. The latter oscillation, to some extent, is very similar to the Rossby index cycle of atmosphere over middle and high latitudes.     

Wavelet fractal character of overlapping signal

A new method based on the combining of the wavelet theory with the fractal theory and named wavelet fractal peak position method (WFPPM) is introduced to extract the number of the components and the relevant peak positions from overlapping signals in chemistry .The overlapping signal is first transformed into continuous wavelet transform value of time domain in certain dilation range via continuous wavelet transform (CWT),and then changed into capacity dimensions (Dc),The number of the components and the relevant positions of overlapping peaks can be identified easily according to the change of Dc.An investigation concerning the influence of different dilation ranges on the peak positions extracted by WFPPM is also provided .Studies show that the WFPPM is an efficient tool for extracting the peak positions and identifying the number of peaks from unresoloved signals,even when this kind of overlapping is significantly serious,Relative errors of lless than 1.0% in peak positions are found when WFPPM is used in the processing of the cadmium (Ⅱ)-indium(Ⅲ) mixture system .The analytical results demonstrate that the desired peak positions can be extracted conveniently ,accurately and rapidly from an unresoled signal via WFPPM,Tremendous developing and applications based on currently reported WFPPM in extracting overlapping signals would be expected in the near future.     

fMRI time series analysis based on stationary wavelet and spectrum analysis

The low signal to noise ratio (SNR) of functional MRI (fMRI) prefers more sensitive data analysis methods. Based on stationary wavelet transform and spectrum analysis, a new method with high detective sensitivity was developed for analyzing fMRI time series, which does not require any prior assumption of the characteristics of noises. In the proposed method, every component of fMRI time series in the different time-frequency scales of stationary wavelet transform was discerned by the spectrum analysis, then the components from noises were removed using the stationary wavelet transform, finally the components of real brain activation were detected by cross-correlation analysis. The results obtained from both simulated and in vivo visual experiments illustrated that the proposed method has much higher sensitivity than the traditional cross-correlation method.     

Feature extraction of gear-localized defect using adaptive lifting scheme and local gradient map

In this paper,the adaptive lifting scheme (ALS) and local gradient maps (LGM) are proposed to isolate the transient feature components from the gearbox vibration signals. Based on entropy minimization rule,the ALS is employed to change properties of an initial wavelet and design adaptive wavelet. Then LGM is applied to characterize the transient feature components in detail signal of decomposition results using ALS. In the present studies, the orthogonal Daubechies 4 (Db 4) wavelet is used as the initial wavelet. The proposed method is applied to both simulated signals and vibration signals acquired from a gearbox for periodic impulses detection. The two conventional methods (cepstrum analysis and Hilbert envelope analysis) and the orthogonal Db4 wavelet are also used to analyze the same signals for comparison. The results demonstrate that the proposed method is more effective in extracting transient components from noisy signals.     

A WT-STFT combining Algorithm

A fast wavelet packet (WP) algorithm is presented, in which the wavelet transform (WT) and the short-time Fourier transform (STFT) are combined. As WT produces multiresolution of frequency and time, and STFT has a fast algorithm, the combining algorithm is suitable for fast signal analysis.     

Analysis of color distortion and optimum fusion for remote sensing images using the statistical property of wavelet decomposition

IHS （Intensity, Hue and Saturation） transform is one of the most commonly used tusion algonthm. But the matching error causes spectral distortion and degradation in processing of image fusion with IHS method. A study on IHS fusion indicates that the color distortion can＇t be avoided. Meanwhile, the statistical property of wavelet coefficient with wavelet decomposition reflects those significant features, such as edges, lines and regions. So, a united optimal fusion method, which uses the statistical property and IHS transform on pixel and feature levels, is proposed. That is, the high frequency of intensity component Ⅰ is fused on feature level with multi-resolution wavelet in IHS space. And the low frequency of intensity component Ⅰ is fused on pixel level with optimal weight coefficients. Spectral information and spatial resolution are two performance indexes of optimal weight coefficients. Experiment results with QuickBird data of Shanghai show that it is a practical and effective method.     

Wavelet transform element of SAW type

This paper proposes to use substrate materials of small electromechanical coupling coefficient k^2 (such as X-112YLiTaO3) to manufacture wavelet transform element of SAW type so as to reduce finger reflections, i.e. to reduce the error of wavelet transform element of SAW type. And it is concluded that the smaller the center frequency of the transmitting IDT of wavelet type, the smaller the error. We suggest to choose substrate material with electromechanical coupling coefficient smaller than that of X-112Y LiTaO3 in the manufacture of the transmitting IDTs of wavelet type and the receiving IDTs at center frequencies above 100MHz, so as to reduce the errors of the transmitting IDTs of wavelet type and the receiving IDTs at center frequencies above 100MHz.     

Testing Jitter on PLL Clocks Based on Analysis of Instantaneous Phase

A novel method based on the analysis of instantaneous phase is proposed to extract the jitter on phase-locked loops output clock. The method utilizes the Hilbert transform to extend the real signal of PLLs output into an analytic signal, and the implementation of Hilbert transform is based on the Fourier transform windowed with Hamming window. Then, the jitter of clock is extracted from the instantaneous phase of analytic signal. The experimental results of simulations validate that the proposed method can effectively extract the jitter on PLL clock, and it has better performance by comparing the sinusoidal jitter extraction results with the other methods.     

Evaluation of earthquake-induced structural damages by wavelet transform

The dynamic behavior of inelastic structures during an earthquake is a complicated non-stationary process that is affected by the random characteristics of seismic ground motions. The conventional Fourier analysis describes the feature of a dynamic process by decomposing the signal into infinitely long sine and cosine series, which loses all time-located information. However, both time and frequency localizations are necessary for the analysis of an evolutionary spectrum of non-stationary processes. In this paper, an analytical approach for seismic ground motions is developed by applying the wavelet transform, which focuses on the energy input to the structure. The procedure of identification of the instantaneous modal parameters based on the continuous wavelet transform (CWT) is given in detail. And then, a novel method using the auto-regressive moving average (ARMA), called "prediction extension”, is presented to remedy the edge effect during the numerical computation of the CWT. The effectiveness of the method is verified by the use of the benchmark model developed by the American Society of Civil Engineers (ASCE). Finally, a scale model with three-storey reinforced concrete frame-share wall structure is made and tested on a shaking table to investigate the relation between the dynamic properties of structures and energy accumulation and its change rates during the earthquake. The results have shown that the wavelet transform is able to provide a deep insight into the identity of transient signals through time-frequency maps of the time variant spectral decomposition.     

Semi-Fragile Watermarking for Copyright Protection and Image Authentication

In this paper, we propose a semi-fragile watermarking technology for copyright protection and image authentication. We transform the image into wavelet domain and group the four adjacent wavelet coefficients. Utilizing the characteristics of tile human visual system, we embed a digital signal into the average of the four adjacent wavelet coefficients since the mean has better ,stability than single wavelet coefficient. This method needn‘t original image when extracts the watermark. Experimental results show the effectiveness of this method which is robust to common image process and fragile to malicious attack.     

Weyl transform associated with wavelets

The Weyl transform on the admissible wavelet space is defined, which is associated with the dilation and translation. And the criteria of its boundedness and compactness on the Lp-spaces are given.     

Ability to detect weak effective seismic signals by utilizing chaotic vibrator system

Taking the advantage of CVS (Chaotic Vibrator System) sensitivity of large-scale periodic phase-state response to quasi-periodic or periodic signals,a series of numerical experiments were made to understand the ability of CVS to detect weak effective seismic signals in the common-shot seismic record distorted by strong stochastic noise. The re-sults demonstrate that the large-scale periodic phase-states of CVS are correlated with the signal composition of the quasi-periodic wavelet sequence constructing from horizontal moveout of seismic events,noise strength and the noise distortion de-gree to signal. For the same kind of events,the higher the noise distortion degree is,the lower the detectable SNR can be reached by CVS. For seismic data with the same noise distortion degree,the closer the scanning seismic velocity (the trial moveout ve-locity) approaches to the accurate velocity,the higher the detectable SNR can be reached by CVS. More-over,the truncating scanning velocities form an asymmetric belt,which indirectly makes CVS achieve a large-scale periodic phase-state and then the ratio of wavelet distortion coefficients in events can be a biggish variable scope.     

Problems in wavelet analysis of hydrologic series and some suggestions on improvement

Applying the wavelet theory and methods to investigate the hydrologic processes such as precipitation and runoff is a hot field. However, several aspects in research are usually ignored: the effect of admissible condition of wavelet functions and the disturbance of noises for the detection of periods, the effect of the length of a hydrologic time-series on the final result, and the choice between the anomaly and the original time series for wavelet analysis. In this paper, these issues are fully discussed. Precipitation data from Lanzhou Precipitation Station are taken for case study. The result indicates that in the wavelet analysis of hydrologic series, denoise methods should be used to eliminate the influence of noises. The MexHat wavelet function satisfies the admissible condition, which ensures that the periodic properties of hydrologic processes can be well represented by using the MexHat wavelet for decomposition. The affected range of hydrologic series which should be discarded before analysis is given. It is also suggested that the anomaly series should be used to highlight the actual undulation of the hydrologic series.     

Application of wavelet transform in runoff sequence analysis

A wavelet transform is applied to runoff analysis to obtain the composition of the runoff sequence and to forecast future runoff. An observed runoff sequence is firstly decomposed and reconstructed by wavelet transform and its expanding tendency is derived. Then, the runoff sequence is forecasted by the back propagation artificial neural networks (BPANN) and by a wavelet transform combined with BPANN. The earlier researches seldom involve the problem of how to choose wavelet function, which is important and cannot be ignored when the wavelet transform is used. With application of the developed approach to the analysis of runoff sequence, several kinds of wavelet functions have been tested.     

Problems in wavelet analysis of hydrologic series and some suggestions on improvement

Applying the wavelet theory and methods to investigate the hydrologic processes such as precipitation and runoff is a hot field. However, several aspects in research are usually ignored: the effect of admissible condition of wavelet functions and the disturbance of noises for the detection of periods, the effect of the length of a hydrologic time-series on the final result, and the choice between the anomaly and the original time series for wavelet analysis. In this paper, these issues are fully discussed. Precipitation data from Lanzhou Precipitation Station are taken for case study. The result indicates that in the wavelet analysis of hydrologic series, denoise methods should be used to eliminate the influence of noises. The MexHat wavelet function satisfies the admissible condition, which ensures that the periodic properties of hydrologic processes can be well represented by using the MexHat wavelet for decomposition. The affected range of hydro-logic series which should be discarded before analysis is given. It is also suggested that the anomaly series should be used to highlight the actual undulation of the hydrologic series.     

On-Chip Built-in Jitter Measurement Circuit for PLL Based on Duty-Cycle Modulation Vernier Delay Line

Phase-locked loops (PLLs) are essential wherever a local event is synchronized with a periodic external event. They are utilized as on-chip clock frequency generators to synthesize a low skew and higher internal frequency clock from an external lower frequency signal and its characterization and measurement have recently been calling for more and more attention. In this paper, a built-in on-chip circuit for measuring jitter of PLL based on a duty cycle modulation vernier delay line is proposed and demonstrated. The circuit employs two delay lines to measure the timing difference and transform the difference signal into digital words. The vernier lines are composed of delay cells whose duty cycle can be adjusted by a feedback voltage. It enables the circuit to have a self calibration capability which eliminates the mismatch problem caused by the process variation.     

A geometric robust watermarking algorithm based on DWT-DCT and Zernike moments

This paper proposed a novel multibits watermarking algorithm providing robustness against geometric attacks. The robustness is achieved from three aspects： （1） Choosing the inscribed disk of the host image as the Zernike moments computation domain and the square in the disk as the watermarking embedding domain. （2） Embedding the watermark in the cascade discrete wavelet transform-discrete cosine transform （DWT-DCT） domain by modulating the specified coefficient pair in each sub block. （3） Saving two selected Zernike moments of the original watermarked image to estimate and correct the geometric attacks before watermark extraction. Experimental results show that the proposed algorithm is robust to any angle of rotation attacks and wide range of scaling attacks, and as well, a variety of other attacks such as lossy compression, common signal processing.     

Wavelet-Based Denoising Attack on Image Watermarking

In this paper, we propose wavelet-based denoising attack methods on image watermarking in discrete cosine transform (DCT) or discrete Fourier transform (DFT) domain or discrete wavelet transform (DWT) domain. Wiener filtering based on wavelet transform is performed in approximation subband to remove DCT or DFT domain watermark, and adaptive wavelet soft thresholding is employed to remove the watermark resided in detail subbands of DWT domain.