A sampling greedy average regularized Kaczmarz method for tensor recovery

Recently, a regularized Kaczmarz method has been proposed to solve tensor recovery problems. In this article, we propose a sampling greedy average regularized Kaczmarz method. This method can be viewed as a block or mini-batch version of the regularized Kaczmarz method, which is based on averaging several regularized Kaczmarz steps with a constant or adaptive extrapolated step size. Also, it is equipped with a sampling greedy strategy to select the working tensor slices from the sensing tensor. We prove that our new method converges linearly in expectation and show that the sampling greedy strategy can exhibit an accelerated convergence rate compared to the random sampling strategy. Numerical experiments are carried out to show the feasibility and efficiency of our new method on various signal/image recovery problems, including sparse signal recovery, image inpainting, and image deconvolution.