Browsing by Subject "Wavelets (Mathematics)"
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Item Adaptive wavelet filter design for optimized image source encoding(Texas Tech University, 2002-12) Kumar, RoopeshDespite intensive research being conducted on the topic of adaptive filter design in general, adaptive filter design in the discrete wavelet transform (DWT) domain with specific constraints is still an active research area. The present work investigates the advantages and limitations of the design of a 2-chanel perfect-reconstruction wavelet filter which is adapted and optimized under minimum energy constraints in a specific band. Such a filter can be used with a quantizer and entropy encoder of a wavelet based image encoder to give optimum performance. An optimal 2-channel conjugate quadrature filter (CQF) bank has been designed and optimized using Sequential Quadratic Programming methods. The filter bank problem is solved using recently developed optimization techniques for general nonlinear, non-convex functions. The results indicate an improved performance for this method compared to the earlier-used Interior-Point optimization method.Item Item Codebook ordering for vector quantization(Texas Tech University, 2003-12) Ye, Linning; Mitra, Sunanda; Nutter, Brian; Karp, TanjaAddress predictive vector quantization (APVQ) utilizes an ordered codebook to exploit the dependency among close input vectors. The Kohonen algorithm is often chosen in APVQ. However, the Kohonen algorithm is not applicable while a codebook already exists. In this thesis three methods of ordering an existing codebook have been developed. Theoretically these codebook ordering methods can be utilized in any vector quantization in order to reduce the output bit rate. Here we apply it to two types of vector quantization approaches, geometric vector quantization (GVQ) and vector quantization based on the LBG algorithm. The results of codebook ordering on vector quantization based on the LBG algorithm are quite good. However, codebook ordering does not have good performance on GVQ. Therefore, while applying codebook ordering to one specific VQ, we should consider the property of this VQ in order to achieve a satisfactory result.Item Color image compression using wavelet transform(Texas Tech University, 1997-08) Meadows, Steven CarlC language coding of image compression algorithms can be a difficult and tedious task. Image compression methods are usually composed of many stages of cascaded algorithms. Each algorithm may be developed independently. This thesis will address the problem of interfacing new image compression algorithms with older and established algorithms such as entropy coding and the discrete wavelet transform. The thesis will describe ANSI C coding procedures and functions involved in implementing two entrop\ coding algorithms including Huffman coding and arithmetic coding. Wavelet theory will be discussed as it applies to the discrete wavelet transform. The thesis will also describe an ANSI C coding implementation of one of the newest wavelet coefficient coding techniques, embedded zerotree wavelets (EZW) developed by Jerome Shapiro. The EZW compression performance will be compared with JPEG which is the standard adapted currently for still images by the Joint Photographic Experts Group.Item Fingerprint image restoration using wavelet transformation(Texas Tech University, 1996-05) Liu, Ti-chungImage compression plays a crucial role m many unportant and diverse applications requiring efficient storage and transmission. This work mainly focuses on a wavelet transform(WT) based compression of fingerprint images and the subsequent classification of the reconstructed images. The algorithm developed involves multiresolution wavelet decomposition, uniform scalar quantization, entropy and run-length encoder/decoder and K-means clustering of the invariant moments as fingerprint features. The performance of the WT-based compression algorithm has been compared with JPEG current image compression standard. Simulation results show that WT outperforms JPEG in high compression ratio region and the reconstructed fingerprint image yields proper classification.Item Methods of dynamical systems, harmonic analysis and wavelets applied to several physical systems(2002) Petrov, Nikola Petrov; Llave, Rafael de laItem Multisensor image fusion(Texas Tech University, 1998-12) Vantipalli, Ravikrishna VIn recent years, a new discipline called multisensor data fusion has been developed to solve a diverse set of problems having common characteristics. Multisensor fusion seeks to combine data from multiple sensors to perform inferences that may not be possible from a single sensor alone. Several image fusion techniques are available, viz. statistical methods, feature selection methods, neural networks, and pyramidal methods. In this thesis fusion is performed using wavelets. The wavelet-based fusion techniques have the advantage of processing different frequency ranges differently, while providing a fast way to integrate local spatial information, a good control over noise, and an easy way to reconstruct the final product. This thesis reviews common image fusion techniques and describes the implementation of the wavelet based image fusion algorithm. The results obtained by applying different fusion schemes in the wavelet domain are presented and compared with those obtained by application of fusion schemes in the spatial domain. Edge detection is performed to show the additional features obtained in the fused images.Item Performance analysis from rate distortion theory of wavelet domain vector quantization encoding(Texas Tech University, 2002-05) Yang, ShuyuVector quantization can be addressed from two major optimization criteria: efficient codebook generation by clustering algorithms with global solutions and optimal encoding with die codebook. Both have been under intense study in recent years. This dissertation gives an in-depth analysis of three well-known clustering algorithms from three different theoretical frameworks in their application to vector quantization. Their efficiencies for codebook training are analyzed and compared with lower bounds from rate-distortion theory. Such an analytical study provides guidelines on the selection of a proper clustering algorithm for vector quantization codebook training. With the codebook generated from a chosen clustering algorithm, a novel hybrid quantization scheme to preserve detail information of an image is also proposed in this dissertation. Motivated by the efficiency of the zerotree scalar coding of wavelet transform coefficients, such as the embedded zerotree wavelet (EZW) and set partitioning in hierarchical trees (SPIHT) algorithms, several attempts have been made recently to adopt similar methodologies to discard insignificant coefficients (or zerotrees) prior to employing traditional vector partitioning. This latter approach to combine vector quantization with zerotree elimination, however, fails to retain fine details, e.g., edge information, with a reasonable codebook size. In the proposed scheme, edge information can be preserved without excessive increase in the codebook size by creating a universal codebook with a combination of vector quantization and residual scalar coding of a few large magnitude wavelet coefficients. The efficiency of this hybrid multiscale vector quantizer (HMVQ) for medical images is demonstrated by encoding MR images and achieving at least 2 dB PSNR improvement over SPIHT at low bit rates. Preservation of fine details even at low bit rates is a desirable characteristic of HMVQ, particularly when medical image coding is concerned. The performance of HMVQ by using a preliminary universal codebook in decoding images with less distortion than the SPIHT decoder at low bit rates is also presented.Item Statistical techniques for identification of coherent structures by wavelet analysis(Texas Tech University, 1998-05) Gilliam, Xiaoning LiWavelet analysis is a rapidly developing area of mathematical and application-oriented research in many disciplines of science and engineering. The wavelet transform, which localizes signals in space and scale, has become a popular tool for analyzing and understanding coherent structures in random fluid flows, especially in the atmospheric boundary layer. In this dissertation, a statistical technique is developed to separate coherent structures in the wavelet transform from fluctuations due to incoherent noise. This technique (coherent structure detector) is based on one of the oldest methods in nonparametric statistics: the development of a randomized reference distribution. To build our randomized reference distribution, we first calculate the Discrete Fourier Transform of the signal. From this, we build a large number of exemplars by keeping the Fourier transform magnitude but randomizing the phase. Thus each exemplar has exactly the same power spectrum as the signal but is known to be incoherent. Each exemplar is then wavelet transformed to provide incoherent transform exemplars. At each scale order statistics are accumulated from the group of wavelet transform exemplars. These order statistics are used to provide the thresholds and corresponding p-values at each scale. This provides our statistical test, from which we identify the statistically significant information in the signal.Item Wavelet-based compression of infrared images using multiscale edges(Texas Tech University, 2003-05) Madan, Tarun KumarInfrared technology has found many exciting and useful applications in the fields ranging from surveillance to astronomy. Therefore the volume of IR data being collected is increasing rapidly. Thus, there is a strong interest in developing image encoding and compression algorithms, specifically for infrared images. Most compression schemes have been developed for photographic images, and very little study exists on IR image coding. These may not be optimized or even appropriate for Infrared data, because they do not take into consideration the peculiar characteristics of infrared images. For this purpose, we study a compression scheme based on edge detection and noise reduction within the wavelet framework. We begin by analyzing the effectiveness of wavelet based multi-scale edge scheme proposed by Mallat and Zhong [1] for compression and noise removal, and optimize it to suit the characteristics of infrared images.Item Wavelets and turbulence(Texas Tech University, 1999-05) Kwan, Johnny Chun ManIn this thesis, the issue of estimating intermittency rates in localized phenomena using wavelets will be addressed. This problem was earlier addressed by Gamage and Hagelberg in [6,8,9]. Here we present an approached based on coherent structure detection. The statistical problem is different from detecting single events, in which the false alarm rate (concluding the signal is coherent when it is actually not) or the size of the test must be controlled for the entire time series. Our new statistical technique controls the false alarm rate for each scale at each time sample, thereby controlling the total false alarm intermittency rate. This is done with a scale-dependent threshold for the wavelet coefficients, which allows two conclusions: that a signal contains intermittent localized phenomena, and that these phenomena are localized to specific time intervals in the signal. The algorithm is statistically rigorous and appropriate for long time series.