期刊
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
卷 49, 期 11, 页码 4177-4193出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TGRS.2011.2141672
关键词
Alternating optimization; endmember extraction; hyperspectral imaging; projected subgradient method; robust optimization; simplex volume maximization; successive optimization
类别
资金
- Hong Kong Research Grant Council [CUHK415509]
- National Science Council (R.O.C.) [NSC 99-2221-E-007-003-MY3, NSC 96-2628-E-007-003-MY3]
In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximum-volume simplex whose vertices are drawn from the pixel vectors. Winter's belief has stimulated much interest, resulting in many different variations of pixel search algorithms, widely known as N-FINDR, being proposed. In this paper, we take a continuous optimization perspective to revisit Winter's belief, where the aim is to provide an alternative framework of formulating and understanding Winter's belief in a systematic manner. We first prove that, fundamentally, the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers but also necessary. Then, under the umbrella of the Winter problem, we derive two methods using two different optimization strategies. One is by alternating optimization. The resulting algorithm turns out to be an N-FINDR variant, but, with the proposed formulation, we can pin down some of its convergence characteristics. Another is by successive optimization; interestingly, the resulting algorithm is found to exhibit some similarity to vertex component analysis. Hence, the framework provides linkage and alternative interpretations to these existing algorithms. Furthermore, we propose a robust worst case generalization of the Winter problem for accounting for perturbed pixel effects in the noisy scenario. An algorithm combining alternating optimization and projected subgradients is devised to deal with the problem. We use both simulations and real data experiments to demonstrate the viability and merits of the proposed algorithms.
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