Michael K. Ng

TL;DR: In this article, a novel generalized BFGS method is proposed for large-scale image restoration minimization problems, where the complexity per step is O(nlogn) operations and only O(n) memory allocations are required, where n is the number of image pixels.

TL;DR: The regularization of the weighted total least squares problem is based on the Tikhonov regularization, and numerical examples are presented to demonstrate the effectiveness of the RWTLS method.

TL;DR: This work proposes to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank Tensor factorization model for low-rank tensor completion problem and develops an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm.

TL;DR: This paper presents a new approach to discovery of periodic patterns from time- series with trends based on time-series decomposition, and shows that this approach is more flexible and suitable to mine periodic patternsFrom time- Series with trends than the previous reported methods.

TL;DR: Theoretically, it is proved that the generalization preserves the diagonalizability and the identity-plus-low-rank decomposition and numerical results are reported to confirm the efficiency of the proposed preconditioner and to show that thegeneralization improves the performance of block circulant preconditionser.