Think big, solve small: Scaling up robust PCA with coupled dictionaries

Recent advances in robust principle component analysis offers a powerful method for solving a wide variety of low-level vision problems. However, if the input data is very large, especially when high-resolution images are involved, it makes RPCA computationally prohibitive for many real applications. To tackle this problem, we propose a fixed-rank RPCA method that uses coupled dictionaries (FRPCA-CD) to handle high-resolution images. FRPCA-CD downsamples high-resolution images into low-resolution images, performs FRPCA on the low-level images to obtain the low-rank matrix, which is reconstructed at original resolution by coupled dictionaries. Comprehensive tests performed on video background recovery, noise reduction in photometric stereo, and image reflection removal problems show that FRPCA-CD can reduce computation time and memory space drastically without sacrificing accuracy.

[1]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[2]  In-So Kweon,et al.  Partial Sum Minimization of Singular Values in RPCA for Low-Level Vision , 2013, 2013 IEEE International Conference on Computer Vision.

[3]  Chun Qi,et al.  Face hallucination based on PCA dictionary pairs , 2013, 2013 IEEE International Conference on Image Processing.

[4]  Takeo Kanade,et al.  Robust L/sub 1/ norm factorization in the presence of outliers and missing data by alternative convex programming , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[5]  Xiaodong Li,et al.  Stable Principal Component Pursuit , 2010, 2010 IEEE International Symposium on Information Theory.

[6]  W. Eric L. Grimson,et al.  Adaptive background mixture models for real-time tracking , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[7]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[8]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[9]  Yuan Cheng,et al.  Background Recovery by Fixed-Rank Robust Principal Component Analysis , 2013, CAIP.

[10]  Kiyoharu Aizawa,et al.  Robust photometric stereo using sparse regression , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  Thomas S. Huang,et al.  Coupled Dictionary Training for Image Super-Resolution , 2012, IEEE Transactions on Image Processing.

[12]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[13]  Mohammad Reza Mohammadi,et al.  PCA-based dictionary building for accurate facial expression recognition via sparse representation , 2014, J. Vis. Commun. Image Represent..

[14]  Wee Kheng Leow,et al.  Incremental Fixed-Rank Robust PCA for Video Background Recovery , 2015, CAIP.

[15]  Alex Pentland,et al.  A Bayesian Computer Vision System for Modeling Human Interactions , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Robert J. Woodham,et al.  Photometric method for determining surface orientation from multiple images , 1980 .

[17]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[18]  Guillermo Sapiro,et al.  Learning Robust Low-Rank Representations , 2012, ArXiv.

[19]  Yongtian Wang,et al.  Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery , 2010, ACCV.

[20]  Michael J. Black,et al.  A Framework for Robust Subspace Learning , 2003, International Journal of Computer Vision.

[21]  John Wright,et al.  RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[22]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.