New Wavelet Bases and Isometric Between Symbolic Operators Spaces OpS_(1,δ)~m and Kernel Distributions Spaces

In the fifties. Calderon established a formal relation between svmbol and kernel distribu-tion, but it is difficult to establish an intrinsic relation. The Calderon-Zygmund (C-Z) school studiedrhe C-Z operators, and Hormander. Kohn and Nirenberg, et al. studied the symbolic operators. Herewe apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases.to characterize both symbolic operators spaces OpS~m and kernel distributions spaces with other spacescomposed of some ahnost diagonal matrices. then get an isometric between OpS~m and kernel distri-bution spaces

NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.

Characteristics and method of synthesis seismic wave based on wavelet reconstruction

A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it as criterion, the formula of synthesizing seismic wave is deduced. Using the design parameters specified in Chinese Seismic Design Code for buildings, seismic waves are synthesized. Moreover, the method of selecting wavelet bases in synthesizing seismic wave and the influence of the damping ratio on synthesizing results are analyzed. The results show that the synthesis seismic waves using wavelet bases can represent the characteristics of the seismic wave as well as the ground characteristic period, and have good time-frequency non-stationary.

Entropy of images after wavelet transform

We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.

Genetic Wavelet and Harmonic Waveletand Their Application to Non-stationary Machinery Equipment Diagnosis

The thesis introduces various characteristic wavelet bases used in non-stationary machinery equipment diagnosis, then discusses genetic wavelets and harmonic wavelets and their practical application respectively in fault diagnosis of an internal combustion engine and in orbits extracting (analysis) of rotating machinery.

WAVELET-BASED FAIRING OF B-SPLINE SURFACES

A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduced to approximate a B spline surface by a quasi uniform one. An error control approach for wavelet based fairing is suggested. Samples are given to show the feasibility of the algorithms presented in this paper. The practice showed that the wavelet based fairing is better than energy based one in case where the number of vertices of the B spline surface is greater than 1000. The quantitative variance of the approximation error in accordance with the change of decomposition levels needs to be further explored.

A NEW ADAPTIVE FILTERING SCHEME BASED ON WAVELET TRANSFORM

Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.

FAULT DIAGNOSIS APPROACH FOR ROLLER BEARINGS BASED ON EMPIRICAL MODE DECOMPOSITION METHOD AND HILBERT TRANSFORM

Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.

Feature Extraction and Classification of Plant Leaf Diseases Using Deep Learning Techniques

In India’s economy, agriculture has been the most significantcontributor. Despite the fact that agriculture’s contribution is decreasing asthe world’s population grows, it continues to be the most important sourceof employment with a little margin of difference. As a result, there is apressing need to pick up the pace in order to achieve competitive, productive,diverse, and long-term agriculture. Plant disease misinterpretations can resultin the incorrect application of pesticides, causing crop harm. As a result,early detection of infections is critical as well as cost-effective for farmers.To diagnose the disease at an earlier stage, appropriate segmentation of thediseased component from the leaf in an accurate manner is critical. However,due to the existence of noise in the digitally captured image, as well asvariations in backdrop, shape, and brightness in sick photographs, effectiverecognition has become a difficult task. Leaf smut, Bacterial blight andBrown spot diseases are segmented and classified using diseased Apple (20),Cercospora (60), Rice (100), Grape (140), and wheat (180) leaf photos in thesuggested work. In addition, a superior segmentation technique for the ROIfrom sick leaves with living backdrop is presented here. Textural features of thesegmented ROI, such as 1st and 2nd order WPCA Features, are discoveredafter segmentation. This comprises 1st order textural features like kurtosis,skewness, mean and variance as well as 2nd procedure textural features likesmoothness, energy, correlation, homogeneity, contrast, and entropy. Finally,the segmented region of interest’s textural features is fed into four differentclassifiers, with the Enhanced Deep Convolutional Neural Network provingto be the most precise, with a 96.1% accuracy.

WAVELET METHOD FOR BOUNDARY INTEGRALEQUATIONS

Presents a study which showed how to use wavelet to discretize the boundary integral equations. Application of wavelets to signal and image processing; Kinds of boundary reduction; Sparsity of the matrices in the standard wavelet basis; Methods.

High Performance Algorithms Based on a New Wavelet Expansion for Time Dependent Acoustic Obstacle Scattering

This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchioni and Zirilli[SIAM J.Sci.Comput.,25(2003),1158-1186].The numerical method proposed reduces,via a perturbative approach,the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations.The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved.A computational method has been developed to solve these challenging problems with affordable computing resources.To this aim a new way of using the wavelet transform and new bases of wavelets are introduced,and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way.Several numerical experiments involving realistic obstacles and“small”wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments.To evaluate the performance of the proposed algorithm on parallel computing facilities,appropriate speed up factors are introduced and evaluated.

Speech compression scheme based on wavelet transform and vector quantization

A coding method of speech compression, which is based on Wavlet Transform and Vector Quantization (VQ), is developed and studied. The Wavlet Thansform or Wavlet Packet Thansform is used to process the speech signal, then VQ is used to compress the coefficients of Wavlet Thansform, and the entropy coding is used to decrease the bit rate. The experimental results show that the speech signal, sampled by 8 kHz sampling rate and 8 bit quatisation,i.e., 64 kbit/s bit rate, can be compressed to 6 - 8 kbit/s, and still have high speech quality,and the low-delay, only 8 ms.

Feature extraction for sound source material recognition with impact sounds

Sound source recognition is a part of environmental sound recognition,which is one of the most important research areas in pattern recognition.Impact sounds carry much physical information associated with the sound sources,which makes impact sound based sound source recognition an important approach to improve recognition performance.In this study,the impact sound continuum synthesized with a ball-plate collision model is used for material recognition of the impacted plates.The basis function learning method and time-frequency representation methods,including the short time Fourier transform and the wavelet packet transform,are applied into classification and the recognition results are compared.The result shows that the features obtained by using the basis function learning perform better for material classification of the impacted plates than that by using the short time Fourier transform and the wavelet packet transform.This demonstrates the high efficiency and superiority of this method in material recognition of sound sources.