Robust principal component analysis (RPCA) via decomposition into low-rank plus sparse matrices offers a powerful framework for a large variety of applications such as image processing, video processing, and 3-D computer vision. Indeed, most of the time these applications require to detect sparse outliers from the observed imagery data that can be approximated by a low-rank matrix. Moreover, most of the time experiments show that RPCA with additional spatial and/or temporal constraints often outperforms the state-of-the-art algorithms in these applications. Thus, the aim of this paper is to survey the applications of RPCA in computer vision. In the first part of this paper, we review representative image processing applications as follows: 1) low-level imaging such as image recovery and denoising, image composition, image colorization, image alignment and rectification, multifocus image, and face recognition; 2) medical imaging such as dynamic magnetic resonance imaging (MRI) for acceleration of data acquisition, background suppression, and learning of interframe motion fields; and 3) imaging for 3-D computer vision with additional depth information such as in structure from motion (SfM) and 3-D motion recovery. In the second part, we present the applications of RPCA in video processing which utilize additional spatial and temporal information compared to image processing. Specifically, we investigate video denoising and restoration, hyperspectral video, and background/foreground separation. Finally, we provide perspectives on possible future research directions and algorithmic frameworks that are suitable for these applications.

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On the Applications of Robust PCA in Image and Video Processing

Clutter background suppression and velocity estimation for moving targets are two critical problems in synthetic aperture radar–ground moving target indication (SAR-GMTI). A robust principal component analysis (RPCA) method is used to separate the sparse matrix of moving targets from the low-rank matrix of static backgrounds by using amplitude information in the image domain. However, the nonsparsity of the moving target echoes limits the performance of the RPCA in SAR-GMTI, and the velocity of the moving target cannot be estimated since the phase information is destroyed by the soft-thresholding operator in the RPCA process. To solve these problems, a novel moving target detection method based on RPCA (NRPCA) for SAR systems is proposed in this article. An atomic norm-based optimization program is first constructed to transform the data sparsity requirement into a moving target sparsity requirement. Although this optimization program is NP-hard, it is transformed to semidefinite programming by relaxation. Furthermore, accurate velocity estimation is performed using dual function theory and the alternating direction method of multipliers (ADMM) algorithm while the selection of the sparsity order k is avoided. Simulations and analyses based on experimental data illustrate the effectiveness of the proposed method.

A Novel Moving Target Detection Method Based on RPCA for SAR Systems

Moving targets extraction in multichannel wide-area surveillance system by exploiting sparse phase matrix

The invention provides a missile-borne seeker radar Sigma-Delta-STAP method based on low-rank matrix recovery. The method comprises the steps of (1) establishing a missile-borne seeker radar Sigma-Delta-STAP signal model based on a monopulse guidance system radar, (2) preprocessing sea clutter by adopting the Sigma-Delta-STAP method to generate a distance Doppler data matrix, (3) extracting sparse matrix containing objective components from the distance Doppler data matrix by adopting an RPCA technology, and (4) detecting a movement objective from a distance Doppler spectrogram. According to the method, the missile-borne seeker radar Sigma-Delta-STAP signal model is established based on the monopulse guidance system radar, firstly, the sea clutter is preprocessed by adopting the Sigma-Delta-STAP method, a distance Doppler spectrum after preprocessing by STAP is generated, then, the sparse matrix containing the objective components is extracted from the distance Doppler data matrix by adopting the RPCA technology, and finally the movement objective is effectively detected from the distance Doppler spectrogram.

Missile-borne seeker radar Sigma-Delta-STAP method based on low-rank matrix recovery

We are developing a Moodle plug-in, which is an AES (automated essay scoring) support system for the basic education of university students. Our system evaluates essays based on rubric, which has five evaluation viewpoints “Contents, Structure, Evidence, Style, and Skill”. Vocabulary level is one of the scoring items of Skill. It is calculated using Japanese Language Learners’ Dictionaries constructed by Sunakawa et al. Since this does not fully cover the words used in the student-level essays, we found that there is a problem with the accuracy of the vocabulary level scoring. In this paper, we propose to construct comprehensive Japanese vocabulary difficulty level dictionaries using Japanese Wikipedia as the corpus. We apply Latent Dirichlet Allocation (LDA) to the Wikipedia corpus and find the word appearance probability as one of the indexes of word difficulty. We use the TF-IDF value instead of the LDA value of the words, which rarely appears. As a result, we constructed highly comprehensive Japanese vocabulary difficulty level dictionaries. We confirmed that the vocabulary level can be scored for all words in the test dataset by using the constructed dictionaries.

Proposal of Japanese Vocabulary Difficulty Level Dictionaries for Automated Essay Scoring Support System Using Rubric

Robust PCA has found important applications in many areas, such as video surveillance, face recognition, latent semantic indexing and so on. In this paper, we study its application in ground moving target indication (GMTI) in wide-area surveillance radar system. MTI is the key task in wide-area surveillance radar system. Due to its great importance in future reconnaissance systems, it attracts great interest from scientists. In (Yan et al. in IEEE Geosci. Remote Sens. Lett., 10:617–621, 2013), the authors first introduced robust PCA to model the GMTI problem, and demonstrate promising simulation results to verify the advantages over other models. However, the robust PCA model can not fully describe the problem. As pointed out in (Yan et al. in IEEE Geosci. Remote Sens. Lett., 10:617–621, 2013), due to the special structure of the sparse matrix (which includes the moving target information), there will be difficulties for the exact extraction of moving targets. This motivates our work in this paper where we will detail the GMTI problem, explore the mathematical properties and discuss how to set up better models to solve the problem. We propose two models, the structured RPCA model and the row-modulus RPCA model, both of which will better fit the problem and take more use of the special structure of the sparse matrix. Simulation results confirm the improvement of the proposed models over the one in (Yan et al. in IEEE Geosci. Remote Sens. Lett., 10:617–621, 2013).

https://link.springer.com/content/pdf/10.1007%2Fs40305-013-0006-y.pdf

Leqin Wu

Papers

Robust PCA for Ground Moving Target Indication in Wide-Area Surveillance Radar System