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Research On The Application Of Wavelet Theory In Digital Image Processing And Meshless Methods

Posted on:2009-05-24Degree:DoctorType:Dissertation
Country:ChinaCandidate:D F WuFull Text:PDF
GTID:1118360245463241Subject:Solid mechanics
Abstract/Summary:PDF Full Text Request
Wavelet analysis is a modern subject and has been quickly developed. Wavelet has good localized properties in time domain and frequency domain, therefore it has profound significance in both theory and application. The theory system of the wavelet analysis is formed, and is researched in many fields.Wavelet transform may obtain the multiresolution information of the signal, which accords with general law of human to observe the world. Meanwhile wavelet transform has abundant wavelet base to adapt the signal of different characteristics. Wavelet function and wavelet transform owns perfect mathematics characteristics, which makes wavelet function obatan the favor of the scientists and the engineers increasingly. The application of the wavelet to practical word is more and broader as the wavelet theory research proceeds in last decades. The characteristics of wavelet are as follows:(1) Has the function of the local analysis in time domain and frequency domain.(2) Has the function of the multisolution and multiscale analysis.(3) Is one kind of good nonlinear local base.(4) Has quickly arithmetic based on conjugate mirror image filters. (5) Has variety.(6) New theories continuously appear.Wavelet keeps the characteristic of the time-frequency combined local and multisolution analysis, which deeply changes some traditional method in engineering technology domain. Wavelet theory is a subject with strong applicability from the day of emergence. Presently, wavelet is applied to compress coding, digital filter, edge detection, digital watermarking, remote sensing image fusion, geophysical exploration, medical assay, chemical detection, engineering calculation, control theory, speech synthesis, financial prediction etc.As thorough research to wavelet, several excellent characteristics are hardly united. Especially in the digital image, Orthogonal, symmetrical and compactly support are all important. In this condition, some scholars put forward the idea of the multiwavelet. Multiwavelet not only keeps many advantages of scalar wavelet, but also avoids disadvantages of scalar wavelet. And it can satisfy with many important characteristics, such as smooth, compactly support, symmetry. These characters are propitious to the image compression and reconstruction.Thereinafter, seven parts of content are researched in this paper:The first section, the theory of scalar wavelet and multi-wavelet, iris identification and image processing are introduced.The second section, the basic theory of scalar wavelet analysis is briefly introduced, the relational theory of multi-wavelet is detailed explained, which includes the background, definition, MRA and scale function of multi-wavelet. Some mathematical characteristic is discussed, the way of matrix extension is used to construct multi-wavelet.The third section, meshless method is introduced by the numbers. Meshless method comes forth before thirty years. Then finite element gains enormous success, and meshless method lentamente develops. As the development of the finite element, this method is not perfect. Due to the limitation, the finite element encounters difficulties in the question of stamping big deformation, particle high velocity impact, crack propagation, fluid-solid coupling.In meshless method, the process of forming the approximate function is based on a series of nodes, which not only avoids the complex course of the mesh generation, but also barge up against mesh distortion. Therefore, this method has important research value and application value.The fourth section, correlative content of image processing and application of wavelet and multi-wavelet in image processing are expatiated.The correlative content is introduced, and the application of the wavelet analysis and multiwavelet is expatiate. Further more, to compare the effect of wavelet, multiwavelet and balance multiwavelet using simulation experiment, we draw the conclusion: multiwavelet is better than wavelet in the compress effect generally, but the pre-filter influence the result. The balance multiwavelet need not pretreatment, so it is best of the three method. But it is hard to construct the balance multiwavelet.Iris identification system, iris identification technology and the performance index of the iris identification are introduced. And this paper introduces wavelet analysis into iris identification technology.Nowadays, iris identification technology includes four steps: iris image capture, image pre-processing, iris feature capture, matching and identification. Iris image is captured by special CCD. In the process of image pre-processing, confirming the inside and outside boundary is firstly done, and then the iris images are normalized into rectangular textures. Multi-wavelet is used in the process of picking up iris feature, and then the image is compressed and coding. Finally, the image and stylebook in swatch-base are compared, and drawing the conclusion.The fifth section, meshless method is introduced by the numbers. And the weight function is researched. In the numerical experiment, the effect of normal weight function is discussed, and then several parameters are confirmed.The sixth section, this paper presents meshless method based on wavelet function, and this method combines the compact support of the wavelet function with the meshless method which can eliminate some or all the grids and improves the accuracy. This paper adopts Daubechies as basis function, builds the field function, and obtains the corresponding control equation. An example shows that wavelet meshless method results and exact results are similar, and there is no addition computing time using wavelet meshless method in comparison with the finite element method. The results validate the effectiveness of the wavelet meshless method.Finally, the last section is summarization and expectation.
Keywords/Search Tags:Wavelet, Multiwavelet, Image Processing, Iris Identification, Meshless Method
PDF Full Text Request
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