Mathematical Problems in Engineering / 2015 / Article / Alg 1

Research Article

Backtracking-Based Simultaneous Orthogonal Matching Pursuit for Sparse Unmixing of Hyperspectral Data

Algorithm 1

BSOMP for hyperspectral sparse unmixing.
Part 1 (SOMP):
(1) Initialize hyperspectral data and spectral library
(2) Divide hyperspectral data into several blocks: , and initialize the index set
(3) For each block do
(4)  Set index set and iteration counter . Initialize the residual data of block : ;
(5)  While stopping criterion 1 has not been met do
(6)  Compute the index of the best correlated member of to the actual residual: , where is the
th column of
(7)  Update support set:
(8)  Compute    is the matrix containing the columns of having the indexes from
(9)  Update residual:
(11)  End while
(12)  Set
(13) End for
Part 2 (Backtracking process):
(14) Initialize hyperspectral data , the index set and    is the matrix containing the columns of having
the indexes from
(15) While stopping criterion 2 has not been met do
(16)  Compute solution:
(17)  Compute the member of having the lowest abundance:
(18)  Remove the member having the lowest fractional abundance from the index set and the endmember set:
(20) End while
Part 3 (Abundance estimation):
(21) Estimate abundances using the original hyperspectral data matrix and the endmember set under the constraint of
, subject to .

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