k‐sparse signal recovery via unrestricted ℓ1−2$\ell _{1-2}$‐minimization.

In the field of compressed sensing, ℓ1−2$\ell _{1-2}$‐minimization model can recover the sparse signal well. In dealing with the ℓ1−2$\ell _{1-2}$‐minimization problem, most of the existing literature uses the difference of convex algorithm (DCA) to solve the unrestricted ℓ1−2$\ell _{1-2}$‐minimization model, that is, model (4). Although experiments have proved that the unrestricted ℓ1−2$\ell _{1-2}$‐minimization model can recover the original sparse signal, the theoretical proof has not been established yet. This paper mainly proves theoretically that the unrestricted ℓ1−2$\ell _{1-2}$‐minimization model can recover the sparse signal well, and makes an experimental study on the parameter λ in the unrestricted minimization model. The experimental results show that increasing the size of parameter λ in (4) appropriately can improve the recovery success rate. However, when λ is sufficiently large, increasing λ will not increase the recovery success rate. [ABSTRACT FROM AUTHOR]