by Francis Fuk-sing Wu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves [90]-[94] / LIST OF FIGURES --- p.vii / LIST OF TABLES --- p.ix / NOTATIONS --- p.x / Chapter 1 --- INTRODUCTION / Chapter 1.1 --- Introduction --- p.1-1 / Chapter 1.2 --- Properties of Orthonormal Transforms --- p.1-4 / Chapter 1.3 --- Some Considerations of a Transform System --- p.1-5 / Chapter 1.4 --- Motivation of Work --- p.1-7 / Chapter 1.5 --- Organization of the Thesis --- p.1-9 / Chapter 2 --- COVARIANCE ESTIMATION SCHEMES AND PERFORMANCE COMPARISON OF THE KLT'S / Chapter 2.1 --- Introduction --- p.2-1 / Chapter 2.2 --- Statistics of an Image --- p.2-1 / Chapter 2.3 --- Mathematical Covariance Functions --- p.2-3 / Chapter 2.3.1 --- One-Dimensional : First-Order Markov Model --- p.2-3 / Chapter 2.3.2 --- Two-Dimensional : Separable and Non-Separable Isotropic Models --- p.2-3 / Chapter 2.4 --- Goviance Estimation Schemes --- p.2-5 / Chapter 2.4.1 --- Scheme 1 --- p.2-5 / Chapter 2.4.2 --- Scheme 2 --- p.2-7 / Chapter 2.4.3 --- Scheme 3 --- p.2-8 / Chapter 2.5 --- KLT's of Different Random Processes --- p.2-11 / Chapter 2.6 --- Transform Comparison Based on Real Images --- p.2-14 / Chapter 2.7 --- Concluding Remarks --- p.2-18 / Chapter 3 --- DC TRANSFORMED ENERGY PACKING ABILITY OF KLT AND DCT / Chapter 3.1 --- Introduction --- p.3-1 / Chapter 3.2 --- Analysis of DC Transformed Energy Using Mathematical Covariance Models --- p.3-1 / Chapter 3.2.1 --- First-Order Markov Process --- p.3-1 / Chapter 3.2.2 --- Separable Model --- p.3 -3 / Chapter 3.2.3 --- Non-Separable Isotropic Model --- p.3-4 / Chapter 3.2.4 --- Results --- p.3-5 / Chapter 3.3 --- Chen and Smith Method and Experimental Results --- p.3-7 / Chapter 3.4 --- Concluding Remarks --- p.3-15 / Chapter 4 --- COMPATIBILITY OF THE DCT AND ICT / Chapter 4.1 --- Introduction --- p.4-1 / Chapter 4.2 --- The Discrete Cosine Transform (DCT) --- p.4 -2 / Chapter 4.3 --- The Family of Interger Cosine Transforms (ICT) --- p.4 -3 / Chapter 4.4 --- Analysis of Error Due to Different Forward and Inverse Transforms --- p.4 -8 / Chapter 4.4.1 --- First-Order Markov Process --- p.4-8 / Chapter 4.4.2 --- Separable Model --- p.4-10 / Chapter 4.4.3 --- Non-Separable Isotropic Model --- p.4-12 / Chapter 4.5 --- Results --- p.4-14 / Chapter 4.6 --- Concluding Remarks --- p.4 -18 / Chapter 5 --- ERROR BEHAVIOUR OF THE DCT AND THE ICT / Chapter 5.1 --- Introduction --- p.5 -1 / Chapter 5.2 --- Problem Identification --- p.5 -1 / Chapter 5.2.1 --- Error Distribution and Energy Due to Rounding Operation --- p.5-2 / Chapter 5.2.2 --- Error Distribution and Energy Due to Linear Transformation --- p.5-3 / Chapter 5.2.3 --- Estimation of Residual Error Energy --- p.5-6 / Chapter 5.3 --- Error Energy in the One-Dimensional Order-8 DCT System --- p.5-8 / Chapter 5.4 --- Error Energy in the One-Dimensional Order-8 ICT(4) System --- p.5-11 / Chapter 5.5 --- Error Energy in the Two-Dimensional Order-8 DCT System --- p.5-13 / Chapter 5.6 --- Error Energy in the Two-Dimensional Order-8 ICT(4) System --- p.5-16 / Chapter 5.7 --- Error Energy in Other Transform Systems --- p.5-19 / Chapter 5.7.1 --- Error Energy in the Two-Dimensional Order-16 DCT System --- p.5-20 / Chapter 5.7.2 --- Error Energy in the One-Dimensional Order-16 ICT(7) System --- p.5-21 / Chapter 5.7.3 --- Error Energy in the Two-Dimensional Order-16 ICT(7) System --- p.5 -21 / Chapter 5.8 --- Results --- p.5 -22 / Chapter 5.9 --- Concluding Remarks --- p.5 -24 / Chapter 6 --- CONCLUSIONS --- p.6-1 / Chapter 6.1 --- Summary of Work --- p.6-1 / Chapter 6.2 --- Contribution of the Work --- p.6-2 / Chapter 6.3 --- Recommendation for Further Work --- p.6-3 / Chapter 7 --- REFERENCES --- p.7 -1 / Chapter 8 --- APPENDIX / Chapter A.1 --- Separability of KLTs --- p.A -1 / Chapter A.2 --- Derivation of DCT and KLT DC Transformed Energy --- p.A -2 / First-Order Maikov Process --- p.A -2 / Separable Model --- p.A -3 / Non-Separable Isotropic Model --- p.A -4 / RESULTS