| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 106 === In recent years, fusing a low-spatial-resolution hyperspectral image with a highspatial-resolution multispectral image has been thought of as an economical approach for obtaining high-spatial-resolution hyperspectral image. A fusion criterion, termed
coupled nonnegative matrix factorization (CNMF) has been reported to be effective in yielding promising fusion performance. However, the CNMF criterion amounts to an ill-posed inverse problem. In this thesis, we propose a new data fusion algorithm by suitable regularization that significantly outperforms the unregularized
CNMF algorithm. Besides utilizing the sparsity-promoting regularizer, which promotes the sparsity of the abundance map, we also incorporate the sum-of-squared endmember distances demoting regularizer.
Owing to the bi-convexity of the formulated optimization problem, we can decouple it into two convex subproblems. Each subproblem is then solved by a carefully designed alternating direction method of multiplers (ADMM), leading to a convex-optimization based CNMF (CO-CNMF) fusion algorithm, where each ADMM iterate is equipped with a closed-form solution. Since the problem size is very large, leading to high computational complexity of the proposed CO-CNMF algorithm, we futher obtain alternative expressions by exploiting some inherent matrix structure in those closed-form solutions, which greatly reduce the computational complexity.
Finally, we present some experiments using real hyperspectral data, which can be divided into three parts. The first part is to analyze how we choose parameters in our proposed algorithm. Second, we demonstrate its superior performance to some state-of-the-art fusion algorithms. Third, by some experimental results, we discuss its performance loss due to imperfect co-registration.
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