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Dissertations / Theses on the topic 'MULTIWAVELET'
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Koch, Karsten. "Interpolating scaling vectors and multiwavelets in Rd : a multiwavelet cookery book /." Berlin : Logos-Verl, 2007. http://deposit.d-nb.de/cgi-bin/dokserv?id=2917176&prov=M&dok_var=1&dok_ext=htm.
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Koch, Karsten. "Interpolating scaling vectors and multiwavelets in Rd a multiwavelet cookery book." Berlin Logos-Verl, 2006. http://deposit.d-nb.de/cgi-bin/dokserv?id=2917176&prov=M&dok_var=1&dok_ext=htm.
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Brodin, Andreas. "Multiwavelet analysis on fractals." Doctoral thesis, Umeå : Dept. of Mathematics and Mathematical Statistics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1131.
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Martin, Michael B. "Applications of Multiwavelets to Image Compression." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/33601.
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Methods for digital image compression have been the subject of much study over the past decade. Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry.
However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of these desirable properties. The relatively new field of multiwavelets shows promise in removing some of the limitations of wavelets. Multiwavelets offer more design options and hence can combine all desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms.
This thesis presents new multiwavelet transform methods and measurements that verify the potential benefits of multiwavelets. Using a zerotree quantization scheme modified to better match the unique decomposition properties of multiwavelets, it is shown that the latest multiwavelet filters can give performance equal to, or in many cases superior to, the current wavelet filters. The performance of multiwavelet packets is also explored for the first time and is shown to be competitive to that of wavelet packets in some cases. The wavelet and multiwavelet filter banks are tested on a much wider range of images than in the usual literature, providing a better analysis of the benefits and drawbacks of each.
NOTE: (03/2007) An updated copy of this ETD was added after there were patron reports of problems with the file.<br>Master of Science
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Garcia, Bautista Javier. "Multiwavelet-based hp-adaptation for discontinuous Galerkin methods." Thesis, Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0046.
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L’objectif principal de cette thèse est de développer une méthode hp-adaptative efficace en termes de coût et précision pour les schémas Galerkin discontinus appliqués aux équations de Navier-Stokes, en combinant flexibilité de l’adaptation a posteriori et précision de l’adaptation multi-résolution. Les performances de l’algorithme d’adaptation hp sont illustrées sur plusieurs cas d’écoulements stationnaires en une et deux dimensions. La première direction de recherche emploie une nouvelle méthodologie basée sur les multiondelettes pour estimer l’erreur de discrétisation de la solution numérique dans le contexte de simulations avec adaptation h. Les résultats démontrent clairement la viabilité de cette méthode pour atteindre un gain de calcul significatif par rapport àun raffinement de maillage uniforme. La deuxième voie de recherche aborde l’analyse et le développement d’une nouvelle stratégied’adaptation hp basée sur la décroissance du spectre des multi-ondelettes comme critère adaptation hp. Cette stratégie permet de discriminer avec succès les régions caractérisées par une grande régularité de celles contenant des phénomènes discontinus. De manière remarquable, l’algorithme d’adaptation hp est capable d’atteindre une haute précision caractéristique des solutions numériques d’ordre élevé tout en évitant les oscillations indésirables en adoptant des approximations d’ordre réduit à proximité des singularités<br>The main objective of the present thesis is to devise, construct and validate computationally efficient hp-adaptive discontinuous Galerkin schemes of the Navier-Stokes equations by bringing together the flexibility of a posteriori error driven adaptation and the accuracy of multiresolution-based adaptation. The performance of the hp-algorithm is illustrated by several steady flows in one and two dimensions.The first research direction employs a new multiwavelet-based methodology to estimate the discretization error of the numerical solution in the context of h-adaptive simulations. The results certainly demonstrate the viability of h-refinement to reach a significant computational gain with respect to uniformly refined grids. The second line of investigation addresses the analysis and development of a new hp-adaptive strategy based on the decay of the multiwavelet spectrum to drive hp-adaptive simulations. The strategy successfully discriminates between regions characterized by high regularity and discontinuous phenomena and their vicinity. Remarkably, the developed hp-adaptation algorithm is able to achieve the high accuracy characteristic of high-order numerical solutions while avoiding unwanted oscillations by adopting low-order approximations in the proximity of singularities
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Fann, George I.-Pan. "Efficient multiwavelet representation of the projector on divergence-free functions." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/9176.
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Castrillón, Candás Julio E. (Julio Enrique). "Spatially adaptive multiwavelet representations on unstructured grids with applications to multidimensional computational modeling." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8923.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.<br>Includes bibliographical references (p. 130-134).<br>In this thesis, we develop wavelet surface wavelet representations for complex surfaces, with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. However, we further extend the construction of surface wavelets and prove the existence of a large class of multiwavelets in Rn with vanishing moments around corners that are well suited for complex geometries. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modeling. This motivates the study of surface wavelets as an efficient representation for the modeling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, cast in the integral form. We analyze and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties.<br>(cont.) We show both theoretically and experimentally that an O(h2/n) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN)7/2 N) entries in the discrete operator matrix, where N is the number of unknowns. Moreover our theoretical proof of accuracy vs compression is applicable to a large class of Calderón-Zygmund integral operators. In principle, this convergence analysis may be extended to higher order wavelets with greater vanishing moment. This results in higher convergence and greater compression.<br>by Julio E. Castrillón Candás.<br>Ph.D.
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Jacobs, Denise Anne. "Multiwavelets in higher dimensions." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28780.
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Strela, Vasily. "Multiwavelets--theory and applications." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/10631.
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Iyer, Lakshmi Ramachandran. "Image Compression Using Balanced Multiwavelets." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/33748.
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The success of any transform coding technique depends on how well the basis functions represent the signal features. The discrete wavelet transform (DWT) performs a multiresolution analysis of a signal; this enables an efficient representation of smooth and detailed signal regions. Furthermore, computationally efficient algorithms exist for computing the DWT. For these reasons, recent image compression standards such as JPEG2000 use the wavelet transform.
It is well known that orthogonality and symmetry are desirable transform properties in image compression applications. It is also known that the scalar wavelet transform does not possess both properties simultaneously. Multiwavelets overcome this limitation; the multiwavelet transform allows orthogonality and symmetry to co-exist. However recently reported image compression results indicate that the scalar wavelets still outperform the multiwavelets in terms of peak signal-to-noise ratio (PSNR).
In a multiwavelet transform, the balancing order of the multiwavelet is indicative of its energy compaction efficiency (usually a higher balancing order implies lower mean-squared-error, MSE, in the compressed image). But a high balancing order alone does not ensure good image compression performance. Filter bank characteristics such as shift-variance, magnitude response, symmetry and phase response are important factors that also influence the MSE and perceived image quality.
This thesis analyzes the impact of these multiwavelet characteristics on image compression performance. Our analysis allows us to explain---for the first time---reasons for the small performance gap between the scalar wavelets and multiwavelets.
We study the characteristics of five balanced multiwavelets (and 2 unbalanced multiwavelets) and compare their image compression performance for grayscale images with the popular (9,7)-tap and (22,14)-tap biorthogonal scalar wavelets. We use the well-known SPIHT quantizer in our compression scheme and utilize PSNR and subjective quality measures to assess performance. We also study the effect of incorporating a human visual system (HVS)-based transform model in our multiwavelet compression scheme.
Our results indicate those multiwavelet properties that are most important to image compression. Moreover, the PSNR and subjective quality results depict similar performance for the best scalar wavelets and multiwavelets. Our analysis also shows that the HVS-based multiwavelet transform coder considerably improves perceived image quality at low bit rates.<br>Master of Science
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Zheng, Ellen Yanqing. "A comparative study of wavelets and multiwavelets." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/9651.
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In this thesis, some basic concepts and theorems are studied, leading to the cascade algorithm which is the most usual approximating method used in the construction of wavelets. By considering the symmetry property of scalar wavelets, Lawton's complex-valued scalar wavelets are studied and some recent results are implemented in the theory of complex-valued scalar wavelets. Another important part of this thesis is the study of multiwavelets. Some comparisons are made among real-valued scalar wavelets, complex-valued scalar wavelets and real-valued multiwavelets. A special contribution is the figures of different kinds of wavelets and some numerical results.
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Downie, Timothy Ross. "Wavlet methods in statistics." Thesis, University of Bristol, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389339.
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Nixon, Steven Paul. "Theory and applications of the multiwavelets for compression of boundary integral operators." Thesis, University of Salford, 2004. http://usir.salford.ac.uk/2035/.
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In general the numerical solution of boundary integral equations leads to full coefficient matrices. The discrete system can be solved in O(N2) operations by iterative solvers of the Conjugate Gradient type. Therefore, we are interested in fast methods such as fast multipole and wavelets, that reduce the computational cost to O(N lnp N). In this thesis we are concerned with wavelet methods. They have proved to be very efficient and effective basis functions due to the fact that the coefficients of a wavelet expansion decay rapidly for a large class of functions. Due to the multiresolution property of wavelets they provide accurate local descriptions of functions efficiently. For example in the presence of corners and edges, the functions can still be approximated with a linear combination of just a few basis functions. Wavelets are attractive for the numerical solution of integral equations because their vanishing moments property leads to operator compression. However, to obtain wavelets with compact support and high order of vanishing moments, the length of the support increases as the order of the vanishingmoments increases. This causes difficulties with the practical use of wavelets particularly at edges and corners. However, with multiwavelets, an increase in the order of vanishing moments is obtained not by increasing the support but by increasing the number of mother wavelets. In chapter 2 we review the methods and techniques required for these reformulations, we also discuss how these boundary integral equations may be discretised by a boundary element method. In chapter 3, we discuss wavelet and multiwavelet bases. In chapter 4, we consider two boundary element methods, namely, the standard and non-standard Galerkin methods with multiwavelet basis functions. For both methods compression strategies are developed which only require the computation of the significant matrix elements. We show that they are O(N logp N) such significant elements. In chapters 5 and 6 we apply the standard and non-standard Galerkin methods to several test problems.
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Beegan, Andrew Peter. "Wavelet-based Image Compression Using Human Visual System Models." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/32939.
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Recent research in transform-based image compression has focused on the wavelet transform due to its superior performance over other transforms. Performance is often measured solely in terms of peak signal-to-noise ratio (PSNR) and compression algorithms are optimized for this quantitative metric. The performance in terms of subjective quality is typically not evaluated. Moreover, the sensitivities of the human visual system (HVS) are often not incorporated into compression schemes.
This paper develops new wavelet models of the HVS and illustrates their performance for various scalar wavelet and multiwavelet transforms. The performance is measured quantitatively (PSNR) and qualitatively using our new perceptual testing procedure.
Our new HVS model is comprised of two components: CSF masking and asymmetric compression. CSF masking weights the wavelet coefficients according to the contrast sensitivity function (CSF)---a model of humans' sensitivity to spatial frequency. This mask gives the most perceptible information the highest priority in the quantizer. The second component of our HVS model is called asymmetric compression. It is well known that humans are more sensitive to luminance stimuli than they are to chrominance stimuli; asymmetric compression quantizes the chrominance spaces more severely than the luminance component.
The results of extensive trials indicate that our HVS model improves both quantitative and qualitative performance. These trials included 14 observers, 4 grayscale images and 10 color images (both natural and synthetic). For grayscale images, although our HVS scheme lowers PSNR, it improves subjective quality. For color images, our HVS model improves both PSNR and subjective quality. A benchmark for our HVS method is the latest version of the international image compression standard---JPEG2000. In terms of subjective quality, our scheme is superior to JPEG2000 for all images; it also outperforms JPEG2000 by 1 to 3 dB in PSNR.<br>Master of Science
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Schiavazzi, Daniele. "Redundant Multiresolution Uncertainty Propagation." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3422585.
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Stochastic partial differential equations can be efficiently solved using collocation approaches combined with polynomial expansion in parameter space. Estimators based on these concepts show smaller variance than traditional or stratified Monte Carlo approaches under mild dimensionality. Research efforts in this context are focused on improving the efficiency of these methodologies for high dimensional problems (increasing number of input random variables) or for problems with discontinuous response in parameter space. In the present work, we use Compressive Sampling in order to minimize the number of deterministic computations needed to evaluate expansion coefficients for stochastic responses which are sparse in selected dictionaries of basis. Moreover, multiresolution approximation techniques are extended in the context of non-intrusive uncertainty propagation. Finally, an adaptive Importance Sampling strategy is used where samples are iteratively added to locations containing relevant features of increasingly smaller size. Applications are presented for analytical functions, stochastic differential equations, dynamical systems whose response is discontinuous or characterized by large gradients. Engineering problems involving robust optimization of windmill airfoils and passive damping of structures under uncertainty are also discussed. The last Chapter is devoted to methodologies aiming to restore element conservativeness for numerical and experimental velocity fields.<br>Metodi non intrusivi basati sull’espansione della risposta di un dato sistema nello spazio dei parametri (Chaos expansion methods) consentono di risolvere equazioni differenziali stocastiche con un numero di soluzioni deterministiche minori rispetto ad approcci tradizionali alla Monte Carlo con campionamento classico o stratificato. In tale ambito gli sforzi di ricerca odierni sono volti allo sviluppo di metodologie atte alla riduzione del costo computazionale in problemi caratterizzati da alta dimensionalitá (numero significativo di variabili aleatorie in input) ed al trattamento di problemi con risposta discontinua nello spazio dei parametri. La ricerca condotta si é concentrata sull’utilizzo di recenti tecniche di Compressive Sampling per la minimizzazione del numero di soluzioni deterministiche necessarie alla ricostruzione di risposte dotate di sparsitá secondo un pre-definito dizionario di basi. Inoltre, tecniche di approssimazione multi-risoluzione sono state estese a metodologie non intrusive di propagazione dell’incertezza. Infine, tecniche di Importance Sampling sono state utilizzate per determinare in modo adattativo l’ubicazione di nuovi samples al fine di cogliere le scale maggiormente importanti nelle risposte approssimate. Le metodologie approfondite ed implementate nell’ambito della ricerca svolta sono state applicate ad un insieme di funzioni analitiche, sistemi descritti da equazioni differenziali stocastiche, sistemi dinamici con risposte caratterizzate da elevati gradienti o discontinuitá, problemi ingegneristici con particolare riferimento all’ottimizzazione robusta della performance aerodinamica di profili per pale eoliche e sistemi passivi di smorzamento delle vibrazioni operanti sotto incertezza. Vengono inoltre presentate metodologie atte a ripristinare doti di conservazione di massa in flussi numerici e sperimentali.
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Koch, Karsten [Verfasser]. "Interpolating scaling vectors and multiwavelets in Rd : a multiwavelet cookery book / Karsten Koch." 2007. http://d-nb.info/999923781/34.
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Chen, Chien-Liang, and 陳建良. "Acoustic Echo Cancellation Using Multiwavelet Transform." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/98473635267269342751.
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碩士<br>國立交通大學<br>電機與控制工程學系<br>86<br>This paper investigates a new technique using discrete
multiwavelet transformsin acoustic echo cancellation. Recently,
Geronimo, Hardin, and Massopust constructed two symmetric
scaling functions, two associated wavelets and corresponding
coefficient matricesfrom the theories of fractal interpolation
functions and the notion of multiresolution analysis. In this
paper, we introduce a binary tree-structured multiwavelet
packetcoupled with adaptive filtering and apply it to acoustic
echo cancellation. Based on the multiwavelet packet
decomposition, we derive the condition of complete echo
cancellation. To approach this optimal condition,we propose a
structure-modified multiwavelet packet.Our experiments show that
the structure-modified multiwavelet packetoutperforms the binary
tree-structured one,with both using symmetric scaling functions.
We next derive a measure to check how wellthe optimal condition
is satisfied.Based on this measure,We propose a procedure to
find the optimal coefficient matriceswith asymmetric scaling
functions and associated wavelets in the echo cancellation
problem.We obtain different optimal coefficient matrices forthe
multiwavelet packets with different structures.The experiment
results on echo cancellationusing the optimal coefficient
matrices are presented.Comparisons to other schemesshow that the
structure-modified multiwavelet packetwith optimal coefficient
matrices has the best performance.
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Yao, Kun-Hong, and 姚坤宏. "Multiwavelet-based Image Watermarking Using Coding Scheme." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/29439290793891792815.
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碩士<br>清雲科技大學<br>電機工程所<br>99<br>A wavelet-based watermarking process utilizing improved channel coding techniques is proposed. The image is decomposed by discrete wavelet transform (DWT) and the watermarks are embedded in sub-blocks of the third level by adjusting the coefficients. After data permutation, the watermark tenacity is enhanced by the fault tolerance ability of the convolutional coding schemes. An improved coding structure is presented to obtain double watermark information without increasing the embedded data. Robustness of the watermark can then be increased. The normalized correlation is used to evaluate the correctness of the watermarks that are retrieved from the compressed watermarked images, noise corrupted images and images filtering. Experiment results demonstrate the excellence of the watermarking technique.
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SINDHU, PRINCY. "MRI/PET IMAGE FUSION USING MULTIWAVELET TRANSFORM." Thesis, 2016. http://dspace.dtu.ac.in:8080/jspui/handle/repository/14790.
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Image fusion is the technique of blending multiple images to obtain a fused image with more descriptive and reliable information. The keen motivation behind image fusion is to compound the complementary as well as relevant information of several images captured from a common scene, to generate an image comprising the superior features of source images. With the availability of modern instrumentation (medical imaging tools) and developed technologies, medical image fusion has become a vital tool in medical applications. Medical image fusion is a concept dealing with the idea of improving the image content by fusion of multiple images obtained using various imaging tools such as Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET), Computed Tomography (CT), Single photon Emission Computed Tomography (SPECT). The objective of this project work is to develop a novel fusion algorithm to fuse two different modality images of brain of a patient to obtain a resulting image with more clear view and complete description. In this work, a framework for medical image fusion based on Multi-Wavelet transform is proposed. Multi-Wavelet transform is improvement over traditional scalar wavelet. In the first part of project work, PET and MRI images are aligned with each other. In the second part, two images are decomposed using Discrete Multi-wavelet transform. In third part of work, these decomposition coefficients are merged correspondingly using edge detection method. In fourth part of work, using these new coefficients, inverse wavelet transform is applied to obtain a fused image with better human/machine perception. Several data set for different diseases are experimented on.
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Chang, Yu-Ping, and 張郁屏. "Learning-based Finger-Vein Verification with Multiwavelet Technologies." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/fxkz8n.
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碩士<br>國立清華大學<br>通訊工程研究所<br>106<br>In recent years, the issue of biometrics has attracted attention. Different biometrics have different applications in life. Because finger vein recognition is non-contact in vivo recognition, the possibility of counterfeiting is low, and it is very convenient to use and has high stability. More and more people are interested in finger vein identification, and there are more and more topics related to vein identification. At present, many banks continue to propose vein identification on a continuous basis, which makes deposits and withdrawals more convenient and safer. However, the identification speed, recognition rate, and EER of the intravenous system have received attention from everyone.
However, the feature extraction of veins is related to image processing technology. multiwavelet has many advantages in the image filtering. It can satisfy good characteristics such as orthogonality, symmetry, and short support. This paper uses GHM multiwavelet filter to perform vein images. GHM multiwavelet is based on multi-resolution analysis. Multi-resolution analysis is the use of data fusion and wavelet transform for image edge detection. This feature can make the finger vein image compression and denoising advantages. In addition, multiwavelet combined with multi-scale wavelets can speed up computation.
Although there is progress in finger vein verifications, performance is still room for improvement in finger vein identification system. First, use GHM filtering to extract the characteristics of the finger vein. GHM multiwavelet filter can make the characteristics of the vein obvious, and the operation speed is fast. The second step is to perform machine learning on the filtered finger vein. This step can find out the person's vein map. This paper proposes the LFR (Learning-based Finger-vein recognition) algorithm and uses GHM multiwavelet fusion machine learning to improve the recognition rate of veins and reduce EER.
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Cho, Okkyung. "Construction of compactly supported multiwavelets." 2006. http://purl.galileo.usg.edu/uga%5Fetd/cho%5Fokkyung%5F200608%5Fphd.
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Chen, Yueting. "Handwritten numeral recognition using multiwavelets." Thesis, 2002. http://spectrum.library.concordia.ca/1812/1/MQ72929.pdf.
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In this report, we review different techniques for handwritten numeral recognition. More importantly we develop and test a hand-written numeral recognition system using multiwavelets. Given a black-and-white numeral, we first trace the contour of the numeral. Secondly we normalize and resample the contour points. Thirdly we perform multiwavelet orthonormal shell expansion on the contour points and we get several resolution levels and the average. We use the multiwavelet coefficients as the features to recognize the hand-written numerals. We use the L1 distance as a measure and the nearest neighbour rule as classifier for the recognition. The experimental result shows that it is a feasible way to use multi-wavelet features in handwritten numeral recognition.
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Zhuang, Xiaosheng. "Interpolating refinable function vectors and matrix extension with symmetry." Phd thesis, 2010. http://hdl.handle.net/10048/1224.
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Thesis (Ph. D.)--University of Alberta, 2010.<br>Title from pdf file main screen (viewed on July 30, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.