Non Convex Algorithms for Group Sparse Optimization

Reweighted Lm,p algorithm Smoothed L2,0 algorithm

Description

Non Convex Optimization Algorithms for Group Sparsity
Solves a dummy OFDM sparse channel estimation problem

Reweighted Lm,p algorithm for noiseless case
 min||x||_m,p s.t. y = Ax

Reweighted Lm,p algorithm for noisy case
 min||x||_2,p s.t. ||y - Ax||_q

Smoothed L2,0 algorithm solves a smooth version of
min||x||_2,0 s.t. y = Ax

Reweigted Lm,p is an extension of the Lp algorithm proposed in:
Rick Chartrand and Wotao Yin, "Iteratively reweighted algorithms for compressive sensing", in 33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008

Smoothed L2,0 is the group version of the SL0 algorithm:
Hossein Mohimani, Massoud Babaie-Zadeh, Christian Jutten, "A fast approach for overcomplete sparse decomposition based on smoothed L0 norm", IEEE Transactions on Signal Processing, Vol.57, No.1, January 2009, pp. 289-301

• MATLAB release: MATLAB 7.0.4 (R14SP2)

[xu zhenhua]

thanks!

[uhmn]

thanks, but some errors occur when running demo.m and mpqdemo.m

??? Undefined function or method 'opMatrix' for input arguments of type 'double'.

Error in ==> rwlspq at 26
    AOp = opMatrix(A); clear A

Error in ==> demo at 6
x1 = rwlspq(A,ybar,0.4,3);
 
??? Undefined function or method 'opMatrix' for input arguments of type 'double'.

Error in ==> lmp_re_ls at 29
    AOp = opMatrix(A);

Error in ==> demo at 3
x = lmp_re_ls(A,y,group,2,0.4);
 
??? Undefined function or method 'matrix_normalizer' for input arguments of type 'double'.

Error in ==> GenGroupSparseProblem at 24
    A = matrix_normalizer(B*W);

Error in ==> mpqdemo at 4
[A, y, group, x0] = GenGroupSparseProblem(100, 150, 25, 3); %generates the group sparse problem