Joint L1/Lp-regularized minimization in video recovery of remote sensing based on compressed sensing

L1 regularization and Lp regularization are proposed for processing recovered images based on compressed sensing (CS). L1 regularization can be solved as a convex optimization problem but is less sparse than Lp (0 < p < 1). Lp regularization is sparser than L1 regularization but is more difficult to solve. This paper proposes joint L1/Lp (0 < p < 1) regularization, which combines Lp regularization and L1 regularization. This joint regularization is applied to recover video of remote sensing based on CS. Joint regularization is sparser than L1 regularization but is as easy to solve as L1 regularization. A linearized Bregman reweighted iteration algorithm is proposed to solve the joint L1/Lp regularization problem. The performance and capabilities of the linearized Bregman algorithm and linearized Bregman reweighted algorithm for solving the joint L1/Lp regularization model are analyzed and compared through numerical simulations.