Related papers: Robust CUR Decomposition: Theory and Imaging Appli…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…
Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the…
As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust…
Existing facial image super-resolution (SR) methods focus mostly on improving artificially down-sampled low-resolution (LR) imagery. Such SR models, although strong at handling artificial LR images, often suffer from significant performance…
This work studies the problem of sequentially recovering a sparse vector $x_t$ and a vector from a low-dimensional subspace $l_t$ from knowledge of their sum $m_t = x_t + l_t$. If the primary goal is to recover the low-dimensional subspace…
This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
Camera relocalization has various applications in autonomous driving. Previous camera pose regression models consider only ideal scenarios where there is little environmental perturbation. To deal with challenging driving environments that…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…
We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both…
In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
While invaluable for many computer vision applications, decomposing a natural image into intrinsic reflectance and shading layers represents a challenging, underdetermined inverse problem. As opposed to strict reliance on conventional…
A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…