Open AccessFast solution to nonnegative eigenvalue decomposition for polarimetric SAR
Author(s) -
Liu G. F.,
Li M.,
Wang Y. J.,
Zhang P.
Publication year - 2013
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2012.3281
Subject(s) - eigenvalues and eigenvectors , mathematics , zero (linguistics) , simple (philosophy) , decomposition , iterative method , decomposition method (queueing theory) , algorithm , discrete mathematics , physics , ecology , philosophy , linguistics , epistemology , quantum mechanics , biology
Since the iteration solution to the nonnegative eigenvalue decomposition (NNED) is quite time‐consuming, a fast solution to the NNED is proposed. From mathematical theory, a conclusion is derived that the result of the NNED is the maximal of nonnegative real zero roots which ensure that all principal minors are nonnegative. Then, according to the conclusion, the fast solution is proposed of which the main body is calculating zero roots and choosing the zero root which satisfies the conclusion as the result of the NNED. The fast solution is simple; its result is theoretically accurate and its time consumption is much less than that of the iteration solution. Finally, the advantage of the fast solution is demonstrated by the experimental results.