In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.

This paper aims to solve the problem of the hyperspectral imagery (HSI) demosaicing under a novel subsampling hyperspectral sensing strategy. The existing method utilizes the periodic structure of sub-sampling to estimate a fixed subspace in matrix form from the measurement result, which reduces the representation ability of the subspace in iterations and destroys the intrinsic structure of the tensor. To overcome these drawbacks, we propose a tensor-based HSI demosaicing (T-Hydemosaicing) model with tensor subspace representation, which takes the low-tubal-rankness and the nonlocal self-similarity into account. In particular, we suggest a tensor singular value decomposition based on orthogonal transformation (Tran-based t-SVD) to learn the tensor subspace that possesses a more powerful representation ability. In addition, we develop an effective algorithm to solve the proposed non-convex model under the framework of the proximal alternating minimization (PAM) algorithm. Experiments conducted on simulated datasets illustrate that the proposed method outperforms other comparative methods in both visual and quantitative terms.