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We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization,…

We analyze synthetic aperture radar (SAR) imaging of complex ground scenes that contain both stationary and moving targets. In the usual SAR acquisition scheme, we consider ways to preprocess the data so as to separate the contributions of…

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…

Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Roadway reconfiguration is a crucial aspect of transportation planning, aiming to enhance traffic flow, reduce congestion, and improve overall road network performance with existing infrastructure and resources. This paper presents a novel…

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…

Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…

In the context of online Robust Principle Component Analysis (RPCA) for the video foreground-background separation, we propose a compressive online RPCA with optical flow that separates recursively a sequence of frames into sparse…

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…

In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of…

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…

Robust principal component analysis (RPCA) decomposes an observation matrix into low-rank background and sparse object components. This capability has enabled its application in tasks ranging from image restoration to segmentation. However,…

Most of the real world complex networks such as the Internet, World Wide Web and collaboration networks are huge; and to infer their structure and dynamics one requires handling large connectivity (adjacency) matrices. Also, to find out the…

A novel text data dimension reduction technique, called the tree-structured multi-linear principal component anal- ysis (TMPCA), is proposed in this work. Being different from traditional text dimension reduction methods that deal with the…

Traffic forecasting is of great importance to transportation management and public safety, and very challenging due to the complicated spatial-temporal dependency and essential uncertainty brought about by the road network and traffic…

We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting…

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…