Dictionary learning for sparse representation using weighted ℓ1-norm

An efficient algorithm for overcomplete dictionary learning with l
_p
-norm as sparsity constraint to achieve sparse representation from a set of known signals is presented in this paper. The special importance of the ¿p-norm (0 <; ρ <; 1) has been recognized in recent studies on sparse modeling, which can lead a stronger sparsity-promoting solutions than the l
₁
-norm. The l
_p
-norm, however, leads to a nonconvex optimization problem that is difficult to solve efficiently. In this paper, the hierarchically alternating update strategy and the weighted ¿j-norm method are introduced to the learning procedure which find local optimal at each iteration. This algorithm is validated to be effective in numerical experiments and present the advantages in recovery ratios of dictionary and robustness of noise compared to MOD, K-SVD and FOCUSS-CNDL.