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Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process, since under- or over- estimation of this number may lead to incorrect unmixing for unsupervised methods. In this thesis we introduce a new method for determining the intrinsic dimension, using recent advances in Random Matrix Theory (RMT). This method is not sensitive to non-i.i.d. and correlated noise, and it is entirely unsupervised and free from any user-determined parameters. The new RMT method is mathematically derived, and robustness tests are run on synthetic data to determine how the results are a ected by: image size; noise levels; noise variability; noise approximation; spectral characteristics of the endmembers, etc. Success rates are determined for many di erent synthetic images, and the method is compared to two principal state of the art methods, Noise Subspace Projection (NSP) and HySime. All three methods are then tested on twelve real hyperspectral images, including images acquired by satellite, airborne and land-based sensors. When images that were acquired by di erent sensors over the same spatial area are evaluated, RMT gives consistent results, showing the robustness of this method to sensor characterisics.

by Wai-kuen Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 57). / Chapter Chapter 1 : --- Introduction --- p.1 / Chapter Chapter 2 : --- Estimation of Correlation between Censored and Polytomous Variables --- p.5 / Chapter 2.1 : --- Model --- p.5 / Chapter 2.2 : --- Maximum Likelihood Estimation between a Censored and a Polytomous Variable --- p.7 / Chapter 2.3 : --- Simulation Study --- p.14 / Chapter 2.4 : --- Extension to Several Variables --- p.18 / Chapter Chapter 3 : --- An application -- Correlation Structure Analysis --- p.33 / Chapter 3.1 : --- Model --- p.33 / Chapter 3.2 : --- Two-stage Estimation Procedure --- p.35 / Chapter 3.3 : --- Optimization Procedure --- p.37 / Chapter Chapter 4 : --- Conclusion --- p.40 / Tables --- p.42 / References --- p.57

by Tung-lok Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 57-59. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Full Maximum Likelihood Estimation of the General Model --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Model --- p.4 / Chapter 2.3 --- Identification of the model --- p.5 / Chapter 2.4 --- Maximum likelihood estimation --- p.7 / Chapter 2.5 --- Computational Procedure --- p.12 / Chapter 2.6 --- Tests of Hypothesis --- p.13 / Chapter 2.7 --- Example --- p.14 / Chapter Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Bayesian Analysis of the general model --- p.18 / Chapter 3.3 --- Computational Procedure --- p.22 / Chapter 3.4 --- Test the Compatibility of the Prior Information --- p.24 / Chapter 3.5 --- Example --- p.25 / Chapter Chapter 4 --- Simulation Study --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Simulation1 --- p.27 / Chapter 4.3 --- Simulation2 --- p.30 / Chapter 4.4 --- Summary and Discussion --- p.31 / Chapter Chapter 5 --- Concluding Remarks --- p.33 / Tables / References --- p.57

by Yin-Ping Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 95-96). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Correlation between Polytomous and Interval Data --- p.6 / Chapter 2.1 --- Model --- p.6 / Chapter 2.2 --- Maximum Likelihood Estimation --- p.8 / Chapter 2.3 --- Partition Maximum Likelihood Estimation --- p.10 / Chapter 2.4 --- Optimization Procedure and Simulation Study --- p.18 / Chapter Chapter 3 --- Three-stage Procedure for Covariance Structure Analysis --- p.25 / Chapter 3.1 --- Model --- p.25 / Chapter 3.2 --- Three-stage Estimation Method --- p.26 / Chapter 3.3 --- Optimization Procedure and Simulation Study --- p.38 / Chapter Chapter 4 --- Two-stage Procedure for Correlation Structure Analysis --- p.46 / Chapter 4.1 --- Model --- p.47 / Chapter 4.2 --- Two-stage Estimation Method --- p.47 / Chapter 4.3 --- Optimization Procedure and Monte Carlo Study --- p.50 / Chapter 4.4 --- Comparison of Two Methods --- p.53 / Chapter Chapter 5 --- Conclusion --- p.56 / Tables --- p.58 / References --- p.95

by Wai-chung Lui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 76-82). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the model with one truncated continuous variable and one polytomous variable --- p.6 / Chapter §2.1 --- The model / Chapter § 2.2 --- Likelihood function of the model / Chapter § 2.3 --- Derivatives of F (θ） / Chapter § 2.4 --- Asymptotic properties of the model / Chapter Chapter 3 --- Estimation of the model with one truncated continuous variable and several polytomous variables --- p.22 / Chapter § 3.1 --- The model / Chapter § 3.2 --- Partition Maximum Likelihood (PML) estimation / Chapter § 3.3 --- Asymptotic properties of the PML estimates / Chapter Chapter 4 --- Optimization procedures and Simulation study --- p.43 / Chapter § 4.1 --- Optimization procedures / Chapter § 4.2 --- Simulation study / Chapter Chapter 5 --- Summary and Conclusion --- p.54 / Tables --- p.56 / References --- p.76