published_or_final_version / Mathematics / Master / Master of Philosophy

Digital image compression is more and more in demand as our society becomes more information oriented, with more digital images being acquired, transmitted and stored everyday. Error-free, or non-destructive, image compression is required in applications where the final image is to be analyzed digitally by computers. A new error-free digital image compression algorithm, the Classifying-Sequencing algorithm, is presented in this dissertation. Without the help of any statistics information of the images being processed, this algorithm achieves average bits-per-pixel close to the entropy of the neighboring pixel difference. In other words, the compression results are comparable to the best that a statistics code can achieve. Because this algorithm does not involve statistical modeling, generation of a code book, or long integer/floating point arithmetics, it is simpler and therefore faster than the standard statistics codes, such as Huffman Code or Arithmetic Code. In this dissertation the new algorithm under discussion is tested using seven images, together with several known algorithms. Three lower-order entropies of the image files are also provided for comparisons. Presenting compression results from an isolated algorithm is not sufficiently objective for comparisons between algorithms, as potential discrepancies exist between not only different images but also same images when reproduced from prints. Comparing the results of different algorithms and with the entropy of the neighboring pixel differences on the same images is more objective. When the entropy of an image is high, the compression ratios of all algorithms are likely to be low; and vice versa. Given that it is faster in decoding than in encoding images, the most prospective applications of the Classifying-Sequencing algorithm are in the fields of digital image transmission, distribution and archiving, where the images are likely to be encoded once but decoded many times. It can be easily realized on simple processors, or completely in hardware, due to its simplicity.

Over the past few decades, the demand for digital information has increased drastically. This enormous demand poses serious difficulties on the storage and transmission bandwidth of the current technologies. One possible solution to overcome this approach is to compress the amount of information by discarding all the redundancies. In multimedia technology, various lossy compression techniques are used to compress the raw image data to facilitate storage and to fit the transmission bandwidth. In this thesis, we propose a new approach using algebraic integers to reduce the complexity of the Daubechies-4 (D4) and Daubechies-6 (D6) Lifting based Discrete Wavelet Transforms. The resulting architecture is completely integer based, which is free from the round-off error that is caused in floating point calculations. The filter coefficients of the two transforms of Daubechies family are individually converted to integers by multiplying it with value of 2x, where, x is a random value selected at a point where the quantity of losses is negligible. The wavelet coefficients are then quantized using the proposed iterative individual-subband coding algorithm. The proposed coding algorithm is adopted from the well-known Embedded Zerotree Wavelet (EZW) coding. The results obtained from simulation shows that the proposed coding algorithm proves to be much faster than its predecessor, and at the same time, produces good Peak Signal to Noise Ratio (PSNR) at very low bit rates. Finally, the two proposed transform architectures are implemented on Virtex-E Field Programmable Gate Array (FPGA) to test the hardware cost (in terms of multipliers, adders and registers) and throughput rate. From the synthesis results, we see that the proposed algorithm has low hardware cost and a high throughput rate.

Preclinical micro-computed tomography (microCT) images are of utility for 3D morphological bone evaluation, which is of great interest in cancer detection and treatment development. This work introduces a compression strategy for microCTs that allocates specific substances in different Volumes of Interest (Vols). The allocation procedure is conducted by the Hounsfield scale. The Vols are coded independently and then grouped in a single DICOM-compliant file. The proposed method permits the use of different codecs, identifies and transmit data corresponding to a particular substance in the compressed domain without decoding the volume(s), and allows the computation of the 3D morphometry without needing to store or transmit the whole image. The proposed approach reduces the transmitted data in more than 90% when the 3D morphometry evaluation is performed in high density and low density bone. This work can be easily extended to other imaging modalities and applications that work with the Hounsfield scale. (C) 2015 Elsevier Ltd. All rights reserved.

In this thesis, we investigate the application of compressive sensing and sparse signal processing techniques to image compression and inpainting problems. Considering that many signals are sparse in certain transformation domain, a natural question to ask is: can an image be represented by as few coefficients as possible? In this thesis, we propose a new model for image compression/decompression based on sparse representation. We suggest constructing an overcomplete dictionary by combining two compression matrices, the discrete cosine transform (DCT) matrix and Hadamard-Walsh transform (HWT) matrix, instead of using only one transformation matrix that has been used by the common compression techniques such as JPEG and JPEG2000. We analyze the Structural Similarity Index (SSIM) versus the number of coefficients, measured by the Normalized Sparse Coefficient Rate (NSCR) for our approach. We observe that using the same NSCR, SSIM for images compressed using the proposed approach is between 4%-17% higher than when using JPEG. Several algorithms have been used for sparse coding. Based on experimental results, Orthogonal Matching Pursuit (OMP) is proved to be the most efficient algorithm in terms of computational time and the quality of the decompressed image. In addition, based on compressive sensing techniques, we propose an image inpainting approach, which could be used to fill missing pixels and reconstruct damaged images. In this approach, we use the Gradient Projection for Sparse Reconstruction (GPSR) algorithm and wavelet transformation with Daubechies filters to reconstruct the damaged images based on the information available in the original image. Experimental results show that our approach outperforms existing image inpainting techniques in terms of computational time with reasonably good image reconstruction performance.

The recent advances in sensor and display technologies have brought upon the High Dynamic Range (HDR) imaging capability. The modern multiple exposure HDR sensors can achieve the dynamic range of 100-120 dB and LED and OLED display devices have contrast ratios of 10^5:1 to 10^6:1. Despite the above advances in technology the image/video compression algorithms and associated hardware are yet based on Standard Dynamic Range (SDR) technology, i.e. they operate within an effective dynamic range of up to 70 dB for 8 bit gamma corrected images. Further the existing infrastructure for content distribution is also designed for SDR, which creates interoperability problems with true HDR capture and display equipment. The current solutions for the above problem include tone mapping the HDR content to fit SDR. However this approach leads to image quality associated problems, when strong dynamic range compression is applied. Even though some HDR-only solutions have been proposed in literature, they are not interoperable with current SDR infrastructure and are thus typically used in closed systems. Given the above observations a research gap was identified in the need for efficient algorithms for the compression of still images and video, which are capable of storing full dynamic range and colour gamut of HDR images and at the same time backward compatible with existing SDR infrastructure. To improve the usability of SDR content it is vital that any such algorithms should accommodate different tone mapping operators, including those that are spatially non-uniform. In the course of the research presented in this thesis a novel two layer CODEC architecture is introduced for both HDR image and video coding. Further a universal and computationally efficient approximation of the tone mapping operator is developed and presented. It is shown that the use of perceptually uniform colourspaces for internal representation of pixel data enables improved compression efficiency of the algorithms. Further proposed novel approaches to the compression of metadata for the tone mapping operator is shown to improve compression performance for low bitrate video content. Multiple compression algorithms are designed, implemented and compared and quality-complexity trade-offs are identified. Finally practical aspects of implementing the developed algorithms are explored by automating the design space exploration flow and integrating the high level systems design framework with domain specific tools for synthesis and simulation of multiprocessor systems. The directions for further work are also presented.

by Roland Siu-kwong Ip. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 101-[105]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Image Compression --- p.2 / Chapter 1.2.1 --- Classification of Image Compression --- p.2 / Chapter 1.2.2 --- Lossy Compression Approaches --- p.3 / Chapter 1.3 --- Video Compression --- p.4 / Chapter 1.3.1 --- Video Compression System --- p.5 / Chapter 1.4 --- Stereoscopic Video Compression --- p.6 / Chapter 1.5 --- Organization of the thesis --- p.6 / Chapter 2 --- Motion Video Coding Theory --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Representations --- p.8 / Chapter 2.2.1 --- Temporal Processing --- p.13 / Chapter 2.2.2 --- Spatial Processing --- p.19 / Chapter 2.3 --- Quantization --- p.25 / Chapter 2.3.1 --- Scalar Quantization --- p.25 / Chapter 2.3.2 --- Vector Quantization --- p.27 / Chapter 2.4 --- Code Word Assignment --- p.29 / Chapter 2.5 --- Selection of Video Coding Standard --- p.31 / Chapter 3 --- MPEG Compatible Stereoscopic Coding --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- MPEG Compatibility --- p.36 / Chapter 3.3 --- Stereoscopic Video Coding --- p.37 / Chapter 3.3.1 --- Coding by Stereoscopic Differences --- p.37 / Chapter 3.3.2 --- I-pictures only Disparity Coding --- p.40 / Chapter 3.4 --- Stereoscopic MPEG Encoder --- p.44 / Chapter 3.4.1 --- Stereo Disparity Estimator --- p.45 / Chapter 3.4.2 --- Improved Disparity Estimation --- p.47 / Chapter 3.4.3 --- Stereo Bitstream Multiplexer --- p.49 / Chapter 3.5 --- Generic Implementation --- p.50 / Chapter 3.5.1 --- Macroblock Converter --- p.54 / Chapter 3.5.2 --- DCT Functional Block --- p.55 / Chapter 3.5.3 --- Rate Control --- p.57 / Chapter 3.6 --- Stereoscopic MPEG Decoder --- p.58 / Chapter 3.6.1 --- Mono Playback --- p.58 / Chapter 3.6.2 --- Stereo Playback --- p.60 / Chapter 4 --- Performance Evaluation --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- Test Sequences Generation --- p.63 / Chapter 4.3 --- Simulation Environment --- p.64 / Chapter 4.4 --- Simulation Results --- p.65 / Chapter 4.4.1 --- Objective Results --- p.65 / Chapter 4.4.2 --- Subjective Results --- p.72 / Chapter 5 --- Conclusions --- p.80 / Chapter A --- MPEG ´ؤ An International Standard --- p.83 / Chapter A.l --- Introduction --- p.83 / Chapter A.2 --- Preprocessing --- p.84 / Chapter A.3 --- Data Structure of Pictures --- p.85 / Chapter A.4 --- Picture Coding --- p.86 / Chapter A.4.1 --- Coding of Motion Vectors --- p.90 / Chapter A.4.2 --- Coding of Quantized Coefficients --- p.94 / References --- p.101

by Cheng Shu Ling. / Thesis submitted in: July 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 70-71). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Image Coding Standard: JPEG --- p.1 / Chapter 1.2 --- Video Coding Standard: MPEG --- p.6 / Chapter 1.2.1 --- MPEG history --- p.6 / Chapter 1.2.2 --- MPEG video compression algorithm overview --- p.8 / Chapter 1.2.3 --- More MPEG features --- p.10 / Chapter 1.3 --- Summary --- p.17 / Chapter Chapter 2 --- Error Resiliency --- p.18 / Chapter 2.1 --- Introduction --- p.18 / Chapter 2.2 --- Traditional approaches --- p.19 / Chapter 2.2.1 --- Channel coding --- p.19 / Chapter 2.2.2 --- ARQ --- p.20 / Chapter 2.2.3 --- Multi-layer coding --- p.20 / Chapter 2.2.4 --- Error Concealment --- p.20 / Chapter 2.3 --- MPEG-4 work on error resilience --- p.21 / Chapter 2.3.1 --- Resynchronization --- p.21 / Chapter 2.3.2 --- Data Recovery --- p.25 / Chapter 2.3.3 --- Error Concealment --- p.28 / Chapter 2.4 --- Summary --- p.29 / Chapter Chapter 3 --- Fixed length codes --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Tunstall code --- p.31 / Chapter 3.3 --- Lempel-Ziv code --- p.34 / Chapter 3.3.1 --- LZ-77 --- p.35 / Chapter 3.3.2 --- LZ-78 --- p.36 / Chapter 3.4 --- Simulation --- p.38 / Chapter 3.4.1 --- Experiment Setup --- p.38 / Chapter 3.4.2 --- Results --- p.39 / Chapter 3.4.3 --- Concluding Remarks --- p.42 / Chapter Chapter 4 --- Self-Synchronizable codes --- p.44 / Chapter 4.1 --- Introduction --- p.44 / Chapter 4.2 --- Scholtz synchronizable code --- p.45 / Chapter 4.2.1 --- Definition --- p.45 / Chapter 4.2.2 --- Construction procedure --- p.45 / Chapter 4.2.3 --- Synchronizer --- p.48 / Chapter 4.2.4 --- Effects of errors --- p.51 / Chapter 4.3 --- Simulation --- p.52 / Chapter 4.3.1 --- Experiment Setup --- p.52 / Chapter 4.3.2 --- Results --- p.56 / Chapter 4.4 --- Concluding Remarks --- p.68 / Chapter Chapter 5 --- Conclusions --- p.69 / References --- p.70

随着3D 图形学技术的快速发展，基于细分小波的多分辨率方法受到了越来越多的关注。为了提高运算效率， 一些细分小波采用了厅局部提升用的方法以避免解全局方程组的庞大开销。这种方法虽然极大地提高了小波分解的速度，但也使得这些小波较之一些经典的细分小波在生成曲面的质量上有所不如。在本篇论文里，我们提出了一组新型细分小波。这些小波变换不但保留了"局部提升"波运算速度快，节省内存的优点，在生成模型的质量上也大大提高，接近了经典的全局优化小波。 / 我们构造了极细分小波用于极结构快速简化和重构。极细分小波变换有效地避免Catmull -Clark 细分小波用于极结构时所造成的"皱裙"和鞍点，可以在高度数的异常点区域生成非常自然的二次连续曲面。为了更好的应用于普通的四边形网格曲面，我们还改进了极细分小波使之生成的曲面可以在边界处与Catmull-Clark 细分小波曲面光滑地融合。实验表明我们构造的混合极细分小波不但运算效率高，节省内存，还具有良好的稳定性，生成的曲面质量良好。基于矩阵值细分，我们还构造了一组近似和插值类型的矩阵值小波。由于矩阵值小波变换直接作用于向量，我们可以利用向量中额外的项作为参数以控制生成的多分辨率由面的形状。通过优化这些形状控制参数，我们在保持高效低内存消耗的同时，还可以进一步提高"局部提升"小波曲面的质量。 / 我们还将矩阵值小波应用于3D 模型的几何压缩。为了避免存储形状控制参数所带来的额外消耗，我们采用固定的形状控制参数从而将矩阵值小波简化为一种特殊的标量值小波。实验表明采用我们的小波的压缩方法，其压缩率接近于经典的全局优化小波，远高于"局部提升"小波。其压缩速度则接近于"局部提升"小波，远高于经典的采用全局优化小波。在未来的研究工作中，我们会进一步优化形状控制参数的选择策略，并尝试将其应用范围从目前三角形网格由面扩展到四边形曲面， T 样条曲面以及混合曲面。我们还将研究如何应用己有的小波变换提高多分辨率编辑与动画技术。 / During the rapid development of 3D graphics applications, the wavelet-based multiresolution approaches have attracted more attention because they can effectively reduce the process/storage costs of high-detailed models. For the efficiency, many wavelets are constructed by using local lifting, which makes the fitting quality of results are not good as the usual wavelets with global optimization. On the other hand, once the wavelet transforms were constructed, the multiresolution meshes got by them cannot be adjusted any more. It is important to develop the new adaptive wavelets with better fitting quality, while keeping the high efficiency. In this dissertation, we provide several secondgeneration wavelets with improved fitting qualities, which include the compound biorthogonal wavelets for the hybrid quadrilateral meshes, and the efficient matrix-valued wavelets for complex triangular meshes. / We propose the novel polar subdivision wavelet, which efficiently generate multiresolution the polar structures. Polar structures are the natural representations of the self-revolution structures or high-valence regions of quadrilateral grids. The traditional multiresolution methods for the polar structures often generate deficits caused by high valence vertices. By adopting the polar subdivision and the special lifting operations on the polar structures, our wavelet transforms can generate smooth multiresolution surfaces without ripples and saddle points. To process the hybrid meshes made of quadrilaterals and polar structures, we extend the polar wavelet to the vertices in the circular layers, which makes it possible to fuse the surfaces generated by different wavelet transforms seamlessly. To improve the fitting quality of local lifting wavelets, we extend wavelet constructions from the scalar-valued scheme to the matrix-valued scheme, and propose a family of novel approximate and interpolatory matrix-valued subdivision wavelets. The matrix-valued wavelets are constructed from the refinable basis function vectors, which deal with the additional parameters to the geometric position of vertices. Since the final results of wavelet transforms are sensitive to the parameters, these parameters can be used to adjust the shape of multiresolution surfaces. By applying the lifting scheme, the computations of wavelet transform are local and in-placed. We also discuss the strategy of better shape controls for improving the fitting quality of simplified surfaces. The experiments showed that these novel wavelet transforms were sufficiently stable and performed well for noise reduction. With the suitable shape control parameters, the fitting quality of multiresolution surfaces can be further improved. / We study how to apply the efficient compression approach to the real applications, such as the compression of meshes. Since the shape control parameters need the additional storage, they will decrease the compression ratio if we apply the original versions of matrix-valued wavelets. We revise the construction of the matrix-valued wavelet transform and proposed the parameterized scalar-valued wavelet transform. With the special optimization of wavelet construction and suitable parameters, our compression approach has the high compression ratio close to the well-known approaches using the global orthogonal wavelets, and much higher compression ratio than the compression using the local lifting wavelets, while keeping the good efficiency. In the future work, we plan to extend the matrix-valued wavelets from triangular meshes to quadrilateral, normal and hybrid meshes. We will study how to apply the matrix-valued wavelets to the applications, such as multiresolution editing and animations. Further optimization of the shape control parameters for mobile and online applications is also an important issue. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhao, Chong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 136-149). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Wavelet Transform --- p.4 / Chapter 1.2.1 --- Wavelets and Multiresolution Analysis --- p.4 / Chapter 1.2.2 --- Continuous Wavelet Transforms --- p.7 / Chapter 1.2.3 --- Discrete Wavelet Transform --- p.8 / Chapter 1.3 --- Second Generation Wavelets --- p.9 / Chapter 1.3.1 --- Lifting Scheme --- p.9 / Chapter 1.3.2 --- Subdivision --- p.11 / Chapter 1.3.3 --- Subdivision Wavelets --- p.13 / Chapter 1.4 --- Main Contributions --- p.15 / Chapter 1.5 --- Chapter Summary --- p.16 / Chapter 2 --- Compound Wavelets on Quadrilaterals --- p.18 / Chapter 2.1 --- Introduction --- p.18 / Chapter 2.2 --- Related Work --- p.19 / Chapter 2.3 --- Polar Subdivision --- p.20 / Chapter 2.3.1 --- Subdivision in radial layers --- p.21 / Chapter 2.3.2 --- Subdivision in circular layers --- p.24 / Chapter 2.4 --- Subdivision Wavelets Using Lifting --- p.25 / Chapter 2.4.1 --- Lifting wavelets --- p.25 / Chapter 2.4.2 --- Wavelet transforms --- p.29 / Chapter 2.5 --- Compound Subdivision Wavelets --- p.32 / Chapter 2.6 --- Experimental Results --- p.34 / Chapter 2.7 --- Chapter Summary --- p.38 / Chapter 3 --- Matrix-valued Loop Wavelets --- p.40 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Related Work --- p.41 / Chapter 3.3 --- Matrix-valued Loop Subdivision --- p.43 / Chapter 3.4 --- Matrix-valued Loop Subdivision Wavelet --- p.46 / Chapter 3.4.1 --- Lazy Wavelet --- p.46 / Chapter 3.4.2 --- Inner Product --- p.49 / Chapter 3.4.3 --- Wavelet Transform --- p.54 / Chapter 3.4.4 --- Shape Control Parameters --- p.55 / Chapter 3.5 --- Experiments and Discussion --- p.57 / Chapter 3.6 --- Chapter Summary --- p.61 / Chapter 4 --- Matrix-valued Interpolatory Wavelets --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- Matrix-valued Interpolatory Subdivision --- p.64 / Chapter 4.3 --- Matrix-valued 1-ring Wavelets --- p.67 / Chapter 4.3.1 --- Biorthogonal Wavelet Transform --- p.67 / Chapter 4.3.2 --- Extraordinary Points Treatment --- p.74 / Chapter 4.3.3 --- Shape Control Parameters --- p.75 / Chapter 4.4 --- Matrix-valued 2-ring Wavelets --- p.81 / Chapter 4.5 --- Experiments and Discussion --- p.86 / Chapter 4.5.1 --- 1-ring Wavelet Transform --- p.86 / Chapter 4.5.2 --- 2-ring Wavelet Transform --- p.92 / Chapter 4.6 --- Chapter Summary --- p.98 / Chapter 5 --- Geometry compression using wavelets. --- p.100 / Chapter 5.1 --- Introduction --- p.100 / Chapter 5.2 --- Related Work --- p.101 / Chapter 5.3 --- Matrix-valued Wavelet Transform --- p.105 / Chapter 5.3.1 --- Matrix-valued Loop Subdivision --- p.105 / Chapter 5.3.2 --- Lazy Wavelet --- p.108 / Chapter 5.3.3 --- Inner Product --- p.109 / Chapter 5.3.4 --- Wavelet Transform --- p.112 / Chapter 5.3.5 --- Coding --- p.113 / Chapter 5.4 --- Experiments and discussion --- p.114 / Chapter 5.4.1 --- Stability --- p.117 / Chapter 5.4.2 --- Efficiency --- p.118 / Chapter 5.4.3 --- Compressions --- p.120 / Chapter 5.5 --- Chapter Summary --- p.124 / Chapter 6 --- Conclusions --- p.125 / Chapter 6.1 --- Research Summary --- p.125 / Chapter 6.2 --- Future Work --- p.127 / Chapter A --- Inner Products of Wavelets in Radial Layers --- p.130 / Chapter B --- Publication List --- p.133 / Bibliography --- p.134

by Ho, Hau Lai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 97-103). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of Attractor Image Coding --- p.2 / Chapter 1.2 --- Scope of Thesis --- p.3 / Chapter 2 --- Fundamentals of Attractor Coding --- p.6 / Chapter 2.1 --- Notations --- p.6 / Chapter 2.2 --- Mathematical Preliminaries --- p.7 / Chapter 2.3 --- Partitioned Iterated Function Systems --- p.10 / Chapter 2.3.1 --- Mathematical Formulation of the PIFS --- p.12 / Chapter 2.4 --- Attractor Coding using the PIFS --- p.16 / Chapter 2.4.1 --- Quadtree Partitioning --- p.18 / Chapter 2.4.2 --- Inclusion of an Orthogonalization Operator --- p.19 / Chapter 2.5 --- Coding Examples --- p.21 / Chapter 2.5.1 --- Evaluation Criterion --- p.22 / Chapter 2.5.2 --- Experimental Settings --- p.22 / Chapter 2.5.3 --- Results and Discussions --- p.23 / Chapter 2.6 --- Summary --- p.25 / Chapter 3 --- Attractor Coding with Adjacent Block Parameter Estimations --- p.27 / Chapter 3.1 --- δ-Minimum Edge Difference --- p.29 / Chapter 3.1.1 --- Definition --- p.29 / Chapter 3.1.2 --- Theoretical Analysis --- p.31 / Chapter 3.2 --- Adjacent Block Parameter Estimation Scheme --- p.33 / Chapter 3.2.1 --- Joint Optimization --- p.34 / Chapter 3.2.2 --- Predictive Coding --- p.36 / Chapter 3.3 --- Algorithmic Descriptions of the Proposed Scheme --- p.39 / Chapter 3.4 --- Experimental Results --- p.40 / Chapter 3.5 --- Summary --- p.50 / Chapter 4 --- Attractor Coding using Lapped Partitioned Iterated Function Sys- tems --- p.51 / Chapter 4.1 --- Lapped Partitioned Iterated Function Systems --- p.53 / Chapter 4.1.1 --- Weighting Operator --- p.54 / Chapter 4.1.2 --- Mathematical Formulation of the LPIFS --- p.57 / Chapter 4.2 --- Attractor Coding using the LPIFS --- p.62 / Chapter 4.2.1 --- Choice of Weighting Operator --- p.64 / Chapter 4.2.2 --- Range Block Preprocessing --- p.69 / Chapter 4.2.3 --- Decoder Convergence Analysis --- p.73 / Chapter 4.3 --- Local Domain Block Searching --- p.74 / Chapter 4.3.1 --- Theoretical Foundation --- p.75 / Chapter 4.3.2 --- Local Block Searching Algorithm --- p.77 / Chapter 4.4 --- Experimental Results --- p.79 / Chapter 4.5 --- Summary --- p.90 / Chapter 5 --- Conclusion --- p.91 / Chapter 5.1 --- Original Contributions --- p.91 / Chapter 5.2 --- Subjects for Future Research --- p.92 / Chapter A --- Fundamental Definitions --- p.94 / Chapter B --- Appendix B --- p.96 / Bibliography --- p.97