Spatio-Temporal Adaptive Super-Resolution Reconstruction Model Based on Zemike Moment for Spatial Video Sequences

Video Super-Resolution （SR） reconstruction produces video sequences with High Resolution （HR） via the fusion of several Low-Resolution （LR） video frames. Traditional methods rely on the accurate estimation of subpixel motion, which constrains their applicability to video sequences with relatively simple motions such as global translation. We propose an efficient iterative spatio-temporal adaptive SR reconstruction model based on Zemike Moment （ZM）, which is effective for spatial video sequences with arbitrary motion. The model uses region correlation judgment and self-adaptive threshold strategies to improve the effect and time efficiency of the ZM-based SR method. This leads to better mining of non-local self-similarity and local structural regularity, and is robust to noise and rotation. An efficient iterative curvature-based interpolation scheme is introduced to obtain the initial HR estimation of each LR video frame. Experimental results both on spatial and standard video sequences demonstrate that the proposed method outperforms existing methods in terms of both subjective visual and objective quantitative evaluations, and greatly improves the time efficiency.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.