The $\ell_1-\ell_2$ regularization is a popular nonconvex yet Lipschitz continuous metric, which has been widely used in signal and image processing. The theory for the $\ell_1-\ell_2$ minimization...

The null space property (NSP), which depends only on the null space of the column space of measurement matrix, has received much attention in compressed sensing. This letter considers NSP of the truncated l _1-2 minimization. It provides two versions of NSP of the truncated l _1-2 minimization, under which we present sufficient conditions for the truncated l _1-2 minimization to recover sparse and compressible signals. In addition, we discuss that the truncated l _1-2 stable NSP holds by Gaussian matrices of appropriate sizes with overwhelming probability.

Transformed $L_1$ (TL1) regularization has been shown to have comparable signal recovery capability with $L_1-L_2$ regularization and $L_1/L_2$ regularization, regardless of whether the measurement...