A Fast and Accurate Matrix Completion Method Based on QR Decomposition and L2,1 -Norm Minimization

Robust Tensor Completion via Capped Frobenius Norm

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the lp -norm ( ) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the lp -norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Face2PPG: An Unsupervised Pipeline for Blood Volume Pulse Extraction From Faces

Photoplethysmography (PPG) signals have become a key technology in many fields, such as medicine, well-being, or sports. Our work proposes a set of pipelines to extract remote PPG signals (rPPG) from the face robustly, reliably, and configurably. We identify and evaluate the possible choices in the critical steps of unsupervised rPPG methodologies. We assess a state-of-the-art processing pipeline in six different datasets, incorporating important corrections in the methodology that ensure reproducible and fair comparisons. In addition, we extend the pipeline by proposing three novel ideas; 1) a new method to stabilize the detected face based on a rigid mesh normalization; 2) a new method to dynamically select the different regions in the face that provide the best raw signals, and 3) a new RGB to rPPG transformation method, called Orthogonal Matrix Image Transformation (OMIT) based on QR decomposition, that increases robustness against compression artifacts. We show that all three changes introduce noticeable improvements in retrieving rPPG signals from faces, obtaining state-of-the-art results compared with unsupervised, non-learning-based methodologies and, in some databases, very close to supervised, learning-based methods. We perform a comparative study to quantify the contribution of each proposed idea. In addition, we depict a series of observations that could help in future implementations.

Large-Scale Affine Matrix Rank Minimization With a Novel Nonconvex Regularizer

Low-rank minimization aims to recover a matrix of minimum rank subject to linear system constraint. It can be found in various data analysis and machine learning areas, such as recommender systems, video denoising, and signal processing. Nuclear norm minimization is a dominating approach to handle it. However, such a method ignores the difference among singular values of target matrix. To address this issue, nonconvex low-rank regularizers have been widely used. Unfortunately, existing methods suffer from different drawbacks, such as inefficiency and inaccuracy. To alleviate such problems, this article proposes a flexible model with a novel nonconvex regularizer. Such a model not only promotes low rankness but also can be solved much faster and more accurate. With it, the original low-rank problem can be equivalently transformed into the resulting optimization problem under the rank restricted isometry property (rank-RIP) condition. Subsequently, Nesterov's rule and inexact proximal strategies are adopted to achieve a novel algorithm highly efficient in solving this problem at a convergence rate of O(1/K) , with K being the iterate count. Besides, the asymptotic convergence rate is also analyzed rigorously by adopting the Kurdyka- ojasiewicz (KL) inequality. Furthermore, we apply the proposed optimization model to typical low-rank problems, including matrix completion, robust principal component analysis (RPCA), and tensor completion. Exhaustively empirical studies regarding data analysis tasks, i.e., synthetic data analysis, image recovery, personalized recommendation, and background subtraction, indicate that the proposed model outperforms state-of-the-art models in both accuracy and efficiency.