Matrix Rank Optimization Research Articles

KRMARO: Aerial Detection of Small-Size Ground Moving Objects Using Kinematic Regularization and Matrix Rank Optimization

Detecting moving objects has been well studied in the past due to its importance in computer vision applications. Nevertheless, in aerial imagery, the small sizes of moving objects and the camera motion present challenges to existing well-known detection methods. Most moving object detection methods have reported either high true detection rates associated with high false-detection rates, or low false-detection rates at the expense of lowering true detection rates. This paper proposes a novel method, Kinematic Regularization and Matrix Rank Optimization (KRMARO), to achieve high true-detection rates and reduce false-detection rates significantly. KRMARO introduces a formulation of the moving objects detection problem that integrates a novel kinematic regularization into the principal component pursuit. This formulation models moving objects as sparse, which is located in regions exhibiting unique kinematic properties, while the background is modeled as a low-rank matrix that is corrupted by this sparse. To solve the former formulation accurately, KRMARO proposes a solution based on the inexact Newton method and the inexact augmented Lagrange multiplier with backtracking behavior. The robustness of KRMARO is verified through testing on DARPA VIVID, UCF aerial action, and VIRAT aerial data sets and then comparing the results with relevant state-of-the-art methods.

MARO: matrix rank optimization for the detection of small-size moving objects from aerial camera platforms

Moving objects detection from aerial camera platforms is a very challenging problem due to the small-size of the moving objects and the false motion of the static background elements. Although many methods have been proposed in this domain, they always have a trade-off between true detections and false detections. This paper proposes a novel solution called matrix rank optimization method (MARO) to achieve high true detections with low false detections. In MARO, the detection problem is formulated as a principal component pursuit with a transformation domain. The novelty of MARO is that it solves this problem by using the inexact Newton method and a backtracking behaviour in inexact augmented Lagrange multiplier. MARO has been extensively evaluated using DARPA VIVID, UCF aerial action, and VIRAT aerial datasets. The results show that MARO outperforms current-state-of-the-art methods, as well as lowers the execution time without sacrificing the accuracy.

Non-convex online robust PCA: Enhance sparsity via ℓp-norm minimization

Compressive sensing, matrix rank optimization and Robust PCA-based matrix decomposition have an increasing number of non-convex approaches for optimizing the ideal ℓ0-norm sparsity. This paper presents a novel online non-convex ℓp-norm based Robust PCA (OLP-RPCA) approach, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. Our LP-RPCA method uses a new objective function in the Alternating Direction Method of Multipliers (ADMM) framework to efficiently solve the Robust PCA problem. More importantly, our OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that the computational complexity of our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples. The proposed approaches are evaluated in various applications including Gaussian/non-Gaussian image denoising, face modeling, real-time background subtraction and video inpainting and compared against numerous state-of-the-art low-rank minimization methods to demonstrate the robustness of our algorithms.

Robustness of optimal sensor placement under parametric uncertainty

This paper examines the influence of parametric uncertainties on the optimal sensor placement methodologies for the modal analysis of a truss bridge. Four classical sensor location methodologies are employed: two based on the Fisher information matrix and the other two based on energy matrix rank optimization. Young's modulus, mass density and cross sectional dimensions are considered as uncertain parameters. The independent and cumulative effects of these uncertain variables on the sensor placement are studied. The optimal locations of sensors under parametric uncertainty are assessed with three different criteria: the Fisher matrix determinant, the modal assurance criterion error and the condition number. Furthermore, the robustness of this configuration is investigated for the case of random and bias errors. The numerical results show the parametric uncertainties have significant influence on the optimal sensor configuration of a truss bridge.