| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 104 === This thesis considers a widely studied problem in hyperspectral unmixing---the abundance estimation of hyperspectral images. Abundances are the proportions of different endmembers (the spectral signatures of materials) present in an imaging pixel. Conventionally, these are estimated by solving least-squares problems under the sum-to-one constraint and the non-negativity constraint, known as the fully constrained least squares (FCLS) problem. However, those traditional optimization methods may yield high computational complexity, since the number of spectral bands in hyperspectral images is high (usually several hundreds). Hence, dimension reduction of the data plays a pivotal role in speeding up the unmixing stage. On the other hand, the total number of pixels in the considered image may be very large. Therefore, solving the FCLS problem becomes computationally complex, although it is strictly convex. In this thesis, based on some geometric properties of the abundance estimation problem, we propose a fast abundance estimation algorithm. The main contributions are twofold:
Firstly, we formulate the dimension reduction problem into a matrix factorization problem and solve it by a modified version of the widely known Cholesky factorization technique.
Secondly, we propose a closed-form approximation as the abundance estimates. Due to the simplex structure of the hyperspectral data, most pixels lie within the simplex with vertices being the endmembers, i.e., the convex hull of the endmembers. For those pixels in the simplex, it can be proved that the proposed closed-form abundance approximation exactly yields the global optimum solution to the abundance estimation problem. In addition, the computation of the derived closed-form formula is highly efficient, since some quantities in this formula need to be computed only once, regardless of the number of pixels. Finally, the superior computational efficiency and estimation accuracy of the proposed algorithm over state-of-the-art algorithms are verified through simulations and real data experiments.
|
|---|
