Application of wavelet transform modulus maxima in boundary detection of potential fields

This study presents the use of the method of wavelet transform modulus maxima(WTMM) to detect boundaries of potential field sources.The boundaries of causative sources can be judged by calculating the local modulus maxima of wavelet coefficients at different scales.For the potential field data with noise,the detected boundaries at small scales are easy to be distorted by noise,however,at large scales,the noise can be suppressed greatly and presents more accurate boundary detection results.Therefore,we can get a better boundary judgment by considering the detected boundaries at all scales.Applying the WTMM method to synthetic models and a real data set of Meishan iron deposit,both get a good effect.

Edge Detection of River in SAR Image Based on Contourlet Modulus Maxima and Improved Mathematical Morphology

To cope with the problems that edge detection operators are liable to make the detected edges too blurry for synthetic aperture radar(SAR)images,an edge detection method for detecting river in SAR images is proposed based on contourlet modulus maxima and improved mathematical morphology.The SAR image is firstly transformed to a contourlet domain.According to the directional information and gradient information of directional subband of contourlet transform,the modulus maximum and the improved mathematical morphology are used to detect high frequency and low frequency sub-image edges,respectively.Subsequently,the edges of river in SAR image are obtained after fusing the high frequency sub-image and the low frequency sub-image.Experimental results demonstrate that the proposed edge detection method can obtain more accurate edge location and reduce false edges,compared with the Canny method,the method based on wavelet and Canny,the method based on contourlet modulus maxima,and the method based on improved(ROEWA).The obtained river edges are complete and clear.

An Improved Singularity Computing Algorithm Based on Wavelet Transform Modulus Maxima Method

In order to reduce the hidden danger of noise which can be charactered by singularity spectrum, a new algorithm based on wavelet transform modulus maxima method was proposed. Singularity analysis is one of the most promising new approaches for extracting noise hidden information from noisy time series . Because of singularity strength is hard to calculate accurately, a wavelet transform modulus maxima method was used to get singularity spectrum. The singularity spectrum of white noise and aluminium interconnection electromigration noise was calculated and analyzed. The experimental results show that the new algorithm is more accurate than tradition estimating algorithm. The proposed method is feasible and efficient.

Singularity detection of the thin bed seismic signals with wavelet transform

The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has been found that the locations of singularities after wavelet transform are only affected by two factors, their original locations and the seismic wavelet length, which says it does not matter with what shape the wavelet will be. The wavelet length can be determined according to the wavelet transform results and be eliminated thereafter so that we are able to detect thin bed seismic signal with resolution of l/32 wavelength. The singularities have been recovered with improved resolution of the seismic section by real data processing.

Wavelet Transform Modulus Maxima-Based Robust Digital Image Watermarking in Wavelet Domain

A new robust watermarking approach was proposed in 2D continuous wavelet domain （CWT）. The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima （WTMM） of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.

On Wavelet Transform General Modulus Maxima Metric for Singularity Classification in Mammograms

Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.

Steganography based on wavelet transform and modulus function

In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.

Application of discrete wavelet operations in the detection of acoustic emission of coal and rock rupture

Through the 5-channel SWAES digital full waveform AE detector, the paper dealt with the fracture process of coal and rock samples under uniaxial compression. Using wavelet operations of multi-scale discrete analysis the pulses of a particular time period （points） and the space domain signal by numerical method were gotten, and the paper concluded that the signal singularity in load rupture had closely relations with fracture and uniaxial compression. The detected position and the actual breaking point only differed at one sample point, the relative error was 6.82%, and there was no accumulative error. Thus it provided an effective method to solve the problem of instability analysis of the signal singularity detection and coal-rock compression failure in the whole process.

Image edge detection based on nonsubsampled contourlet transform and mathematical morphology

A novel algorithm for image edge detection is presented. This algorithm combines the nonsubsampled contourlet transform and the mathematical morphology. First, the source image is decomposed by the nonsubsampled contourlet transform into multi-scale and multi-directional subbands. Then the edges in the high-frequency and low-frequency sub-bands are respectively extracted by the dualthreshold modulus maxima method and the mathematical morphology operator. Finally, the edges from the high- frequency and low-frequency sub-bands are integrated to the edges of the source image, which are refined, and isolated points are excluded to achieve the edges of the source image. The simulation results show that the proposed algorithm can effectively suppress noise, eliminate pseudo-edges and overcome the adverse effects caused by uneven illumination to a certain extent. Compared with the traditional methods such as LoG, Sobel, and Carmy operators and the modulus maxima algorithm, the proposed method can maintain sufficient positioning accuracy and edge details, and it can also make an improvement in the completeness, smoothness and clearness of the outline.

Edge detection based on object tree image representation and wavelet transform

In applications such as image retrieval and recognition, precise edge detection for interested regions plays a decisive role. Existing methods generally take little care about local characteristics, or become time consuming if every detail is considered. In the paper, a new method is put forward based on the combination of effective image representation and multiscale wavelet analysis. A new object tree image representation is introduced. Then a series of object trees are constructed based on wavelet transform modulus maxima at different scales in descending order. Computation is only needed for interested regions. Implementation steps are also given with an illustrative example.

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.

P-Wave Detection Combining Entropic Criterion and Wavelet Transform

The objective of this paper is to develop an efficient P wave detection method in electrocardiogram (ECG) using the local entropy criterion (EC) and wavelet transform (WT) modulus maxima. The detection of P wave relates to the diagnosis of many heart diseases and it is also a difficult point during the ECG signal detection. Determining the position of a P-wave is complicated due to the low amplitude, the ambiguous and changing form of the complex. In a first step, QRS complexes are detected using the pan-Tompkins method. Then, we look for the best position of the analysis window and the value of the most appropriate width to the P wave. Finally, the determination of P wave peaks, as well as their onsets and offsets. The method has been validated using ECG-recordings with a wide variety of P-wave morphologies from MIT-BIH Arrhythmia and QT database. The P-wave method obtains a sensitivity of 99.87% and a positive predictivity of 98.04% over the MIT-BIH Arrhythmia, while for the QT, sensitivity and predictivity over 99.8% are attained.

Application of Wavelet Transform Modulus Maxima in Raman Distributed Temperature Sensors

We proposed and demonstrated a wavelet transform modulus maxima （WTMM） de-noising method to decrease the temperature error. In this scheme, the composition scale was determined simply by the WTMM amplitude variation with the growth of the decomposition scale at 30 ℃, and the signal WTMM was obtained by the wavelet decomposition modulus on every decomposition scale based on the modulus propagating difference between the signal and noise. Then, we reconstructed the signal using the signal WTMM. Experimental results show that the proposed method is effective for de-noising, allowing for a temperature error decrease of about 1 ℃ at 40 ℃ and 50℃ comparing to the original data.

Fractal analysis of polyethylene catalysts surface morphologies based on wavelet transform modulus maxima method

Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies.

Classification using wavelet packet decomposition and support vector machine for digital modulations

To make the modulation classification system more suitable for signals in a wide range of signal to noise rate （SNR）, a feature extraction method based on signal wavelet packet transform modulus maxima matrix （WPTMMM） and a novel support vector machine fuzzy network （SVMFN） classifier is presented. The WPTMMM feature extraction method has less computational complexity, more stability, and has the preferable advantage of robust with the time parallel moving and white noise. Further, the SVMFN uses a new definition of fuzzy density that incorporates accuracy and uncertainty of the classifiers to improve recognition reliability to classify nine digital modulation types （i.e. 2ASK, 2FSK, 2PSK, 4ASK, 4FSK, 4PSK, 16QAM, MSK, and OQPSK）. Computer simulation shows that the proposed scheme has the advantages of high accuracy and reliability （success rates are over 98% when SNR is not lower than 0dB）, and it adapts to engineering applications.

Comparative analysis of different methods for image enhancement

Image enhancement technology plays a very important role to improve image quality in image processing. By enhancing some information and restraining other information selectively, it can improve image visual effect. The objective of this work is to implement the image enhancement to gray scale images using different techniques. After the fundamental methods of image enhancement processing are demonstrated, image enhancement algorithms based on space and frequency domains are systematically investigated and compared. The advantage and defect of the above-mentioned algorithms are analyzed. The algorithms of wavelet based image enhancement are also deduced and generalized. Wavelet transform modulus maxima(WTMM) is a method for detecting the fractal dimension of a signal, it is well used for image enhancement. The image techniques are compared by using the mean(μ),standard deviation(?), mean square error(MSE) and PSNR(peak signal to noise ratio). A group of experimental results demonstrate that the image enhancement algorithm based on wavelet transform is effective for image de-noising and enhancement. Wavelet transform modulus maxima method is one of the best methods for image enhancement.

A new iterative algorithm for reconstructing a signal from its dyadic wavelet transform modulus maxima

A new algorithm for reconstructing a signal from its wavelet transform modulus maxima is presented based on an iterative method for solutions to monotone operator equations in Hilbert spaces. The algorithm's convergence is proved. Numerical simulations for different types of signals are given. The results indicate that compared with Mallat's alternate projection method, the proposed algorithm is simpler, faster and more effective.

基于小波变换和GA-BP神经网络的电力电缆故障定位

由于电力电缆敷设于地下,当发生故障时难以快速且准确定位,出现了故障定位问题。因此,提出一种基于小波变换和遗传算法反向传播(Genetic algorithm back propagation,GA-BP)神经网络的电力电缆故障定位方法,在分析对比各小波能量集中程度和波动次数的基础上,选择多贝西小波(Daubechies wavelet 6,Db6)作为小波基函数,对于各故障位置,采集正向故障行波的α模分量,并对其进行小波分解。选取在d1尺度下的模极大值点作为特征值,同时将故障距离作为标签值,从而构建了训练和测试样本数据集;利用遗传算法(Genetic algorithm,GA)的种群进化和全局最优搜寻能力来改善误差逆传播(Back propagation,BP)网络对初始权重敏感的缺点,并使用优化后的权值、阈值重新对BP神经网络进行训练和预测,最后通过与传统双端行波定位算法、BP算法、粒子群优化BP算法(Particle swarm optimization BP,PSO-BP)相比较,证明了所提方法在测距性能方面的优越性。

±800kV直流输电线路雷电绕击与反击的识别方法

研究±800kV直流输电线路雷电绕击和反击故障的机理,建立了绕击和反击的等值电路模型。分析和仿真表明:若发生反击故障,由于杆塔接地电阻的作用,反击故障将包括雷电流入地和随之而来的塔顶电位(绝对值)骤增造成的绝缘子闪络2个过程,对应地,在这2个过程中零模电流的方向相反,使得故障后瞬间保护安装处零模电压出现正负交替;若发生绕击故障,零模电流只沿一个方向,使保护安装处零模电压在故障后一段时间内呈现单调变化。在绕击与反击故障下于保护安装处所观测的零模电压时域特征存在显著差异,在此基础上,从继电保护的角度出发,提出了一种基于小波变换的特高压直流输电线路雷电绕击与反击故障的识别方法,EMTDC仿真表明该方法能对特高压直流全线雷电绕击与反击故障进行识别,且不受雷电流波形的影响。

小波去噪的几种方法

利用小波方法去噪 ,是小波分析应用于工程实际的一个重要方面。该文介绍了几种常用的小波去噪方法 ,分别是小波分解与重构法、非线性小波变换阈值法、平移不变量法和小波变换模极大值法。将上述几种方法分别用于叠加了高斯白噪声的仿真信号的去噪处理 ,并通过对几种方法优缺点的比较 ,为小波去噪的方法选择提供了一个参考依据。