Incoherent Dictionary Learning Method Based on Unit Norm Tight Frame and Manifold Optimization for Sparse Representation

Algorithm 2

Improved IP algorithm: UNTF-IP.

      Input: initial dictionary , , iterations;

      Output:

()    Initialize ;

()    ;

()    ;

()    normalize the columns of ;

()    while    do

()      Compute the reference Gram matrix ;

()      Apply (12) to for decreasing the coherence;

()      Apply SVD to to obtain the matrix which rank is equal to be ;

()      Building the squared-root of to obtain a new dictionary;

()   Compute to obtain the next closest UNTF;

()   Normalize the columns of and ;

()   Update , ;

()   Compute the new mutual coherence ;

()   if    then

()    break;

()   end

() end

() return ;