Related papers: On the Robustness of Cross-Concentrated Sampling f…
M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions…
In Maples et al. (2018) we introduced Robust Chauvenet Outlier Rejection, or RCR, a novel outlier rejection technique that evolves Chauvenet's Criterion by sequentially applying different measures of central tendency and empirically…
The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…
FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we give a comprehensive convergence analysis on the FOCUSS…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of…
In this work, we address the problem of outlier detection for robust motion estimation by using modern sparse-low-rank decompositions, i.e., Robust PCA-like methods, to impose global rank constraints. Robust decompositions have shown to be…
Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended by Pham and Venkatesh to cope with the case where corruption to the CS data is modeled as impulsive…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Real-time end-to-end task scheduling in networked control systems (NCSs) requires the joint consideration of both network and computing resources to guarantee the desired quality of service (QoS). This paper introduces a new model for…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences,…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Compressive sensing (CS) is a data acquisition technique that measures sparse or compressible signals at a sampling rate lower than their Nyquist rate. Results show that sparse signals can be reconstructed using greedy algorithms, often…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm,…