An Extended Reweighted <semantics>ℓ1</semantics> Minimization Algorithm for Image Restoration - Sining Huang; Yupeng Chen; Tiantian Qiao (Mathematics, 2021)
This paper proposes an effective extended reweighted <semantics>ℓ1</semantics> minimization algorithm (ERMA) to solve the basis pursuit problem <semantics><munder>minu∈Rn</munder>{||u||1:Au=f}</semantics> in compressed sensing, where <semantics>A∈Rm×n</semantics>, <semantics>m≪n</semantics>. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve <semantics><munder>minu∈Rn</munder>{<msubsup>||u||pp</msubsup>:Au=f}</semantics> problem, with the weight <semantics>ωi(u,p)=(ε+|ui|2)p/2−1</semantics>. Numerical experiments show that this <semantics>ℓ1</semantics> minimization persistently performs better than other methods. Especially when <semantics>p=0</semantics>, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.