Non Convex Algorithms for Group Sparse Optimization

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