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:

(10)   

(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:

(19)   

(20) End while

Part 3 (Abundance estimation):

(21) Estimate abundances using the original hyperspectral data matrix and the endmember set under the constraint of

  nonnegativity.

   , subject to .