The sparse unmixing problem of greedy algorithms still remains a great challenge at finding an optimal subset of endmembers for the observed data from the spectral library,due to the usually high correlation of the sp...The sparse unmixing problem of greedy algorithms still remains a great challenge at finding an optimal subset of endmembers for the observed data from the spectral library,due to the usually high correlation of the spectral library.Under such circumstances,a novel greedy algorithm for sparse unmixing of hyperspectral data is presented,termed the recursive dictionary-based simultaneous orthogonal matching pursuit(RD-SOMP).The algorithm adopts a block-processing strategy to divide the whole hyperspectral image into several blocks.At each iteration of the block,the spectral library is projected into the orthogonal subspace and renormalized,which can reduce the correlation of the spectral library.Then RD-SOMP selects a new endmember with the maximum correlation between the current residual and the orthogonal subspace of the spectral library.The endmembers picked in all the blocks are associated as the endmember sets of the whole hyperspectral data.Finally,the abundances are estimated using the whole hyperspectral data with the obtained endmember sets.It can be proved that RD-SOMP can recover the optimal endmembers from the spectral library under certain conditions.Experimental results demonstrate that the RD-SOMP algorithm outperforms the other algorithms,with a better spectral unmixing accuracy.展开更多
In this paper,we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.
基金supported by the National Natural Science Foundations of China(Nos.61401200,61201365)
文摘The sparse unmixing problem of greedy algorithms still remains a great challenge at finding an optimal subset of endmembers for the observed data from the spectral library,due to the usually high correlation of the spectral library.Under such circumstances,a novel greedy algorithm for sparse unmixing of hyperspectral data is presented,termed the recursive dictionary-based simultaneous orthogonal matching pursuit(RD-SOMP).The algorithm adopts a block-processing strategy to divide the whole hyperspectral image into several blocks.At each iteration of the block,the spectral library is projected into the orthogonal subspace and renormalized,which can reduce the correlation of the spectral library.Then RD-SOMP selects a new endmember with the maximum correlation between the current residual and the orthogonal subspace of the spectral library.The endmembers picked in all the blocks are associated as the endmember sets of the whole hyperspectral data.Finally,the abundances are estimated using the whole hyperspectral data with the obtained endmember sets.It can be proved that RD-SOMP can recover the optimal endmembers from the spectral library under certain conditions.Experimental results demonstrate that the RD-SOMP algorithm outperforms the other algorithms,with a better spectral unmixing accuracy.
基金Project supported by the National Natural Science Foundation of Chinathe Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry+2 种基金Shanghai's Shuguang Projectthe Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P. R. ChinaPartially supported by the Natural Sciences and Engineering Research Council of Canada
文摘In this paper,we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.