Dense error correction for low-rank matrices via Principal Component Pursuit

Ganesh, Arvind; Wright, John; Li, Xiaodong; Candès, Emmanuel J.; Ma, Yi

doi:10.1109/isit.2010.5513538

Cited by 72 publications

(66 citation statements)

References 14 publications

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“…Algorithms for solving the matrix decomposition problem for M 0 = L 0 +S 0 have been presented in [5] and [15]; however, to our knowledge, no algorithms have been explicitly presented for dealing with the case of matrix decomposition with partial observations and entry-wise inequality constraints. We have extended existing algorithms to efficiently deal with these cases.…”

Section: Equivalent Formulationmentioning

confidence: 99%

Space-time signal processing for distributed pattern detection in sensor networks

Paffenroth

Toit

Scharf

et al. 2012

Signal and Data Processing of Small Targets 2012

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Abstract-A theory and algorithm for detecting and classifying weak, distributed patterns in network data is presented. The patterns we consider are anomalous temporal correlations between signals recorded at sensor nodes in a network. We use robust matrix completion and second order analysis to detect distributed patterns that are not discernible at the level of individual sensors. When viewed independently, the data at each node cannot provide a definitive determination of the underlying pattern, but when fused with data from across the network the relevant patterns emerge. We are specifically interested in detecting weak patterns in computer networks where the nodes (terminals, routers, servers, etc.) are sensors that provide measurements (of packet rates, user activity, central processing unit usage, etc.). The approach is applicable to many other types of sensor networks including wireless networks, mobile sensor networks, and social networks where correlated phenomena are of interest.

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Section: Equivalent Formulationmentioning

confidence: 99%

Space-time signal processing for distributed pattern detection in sensor networks

Paffenroth

Toit

Scharf

et al. 2012

Signal and Data Processing of Small Targets 2012

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“…Low-rank matrix recovery, which called low-rank sparse matrix decomposition (LRSMD) or robust principal component analysis (RPCA) [8], is to recognize the broken elements automatically and recover original matrix when some elements in matrix were broken. The prediction of recovering matrix is that matrix is low-rank or rough low-rank.…”

Section: Model For Low-rank Matrix Recoverymentioning

confidence: 99%

An Improved Algorithm to Enhance Recovery Stability for Low-Rank Image

Lian¹,

Zhao²,

Xu³

2017

dtetr

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Abstract. When recovering original image for low-rank image with noise, the effect usually has not been satisfactory through minimizing matrix nuclear norm to obtain low-rank resolution. Aiming at this problem, we introduced Frobenius norm of low-rank matrix, and combined with original low-rank matrix nuclear nor to form new regular item, and utilized an augmented lagrange multiplier method to resolve the problem after convex relaxation. Through adding 2 F A item on the base of original low-rank image recovery model, we can get better denoising result for low-rank image. The experimental results indicated that, by selecting proper parameters, the improved algorithm has superior recovery result compared to traditional LRMR model on wiping off impulse noise and gaussian noise.

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“…In all the above experiments, we have fixed the value of the parameter λ = 1/ √ m, as suggested by [14]. While this choice promises a certain degree of error correction, it may be possible to correct larger amounts of corruption by choosing λ appropriately, as demonstrated in [26] for instance. Unfortunately, the best choice of λ depends on the input images, and cannot be determined analytically.…”

Section: Quantitative Evaluation With Synthetic Imagesmentioning

confidence: 99%

Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery

Ganesh

Shi

et al. 2011

Lecture Notes in Computer Science

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215

240

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Abstract. We present a new approach to robustly solve photometric stereo problems. We cast the problem of recovering surface normals from multiple lighting conditions as a problem of recovering a low-rank matrix with both missing entries and corrupted entries, which model all types of non-Lambertian effects such as shadows and specularities. Unlike previous approaches that use Least-Squares or heuristic robust techniques, our method uses advanced convex optimization techniques that are guaranteed to find the correct low-rank matrix by simultaneously fixing its missing and erroneous entries. Extensive experimental results demonstrate that our method achieves unprecedentedly accurate estimates of surface normals in the presence of significant amount of shadows and specularities. The new technique can be used to improve virtually any photometric stereo method including uncalibrated photometric stereo.

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Dense error correction for low-rank matrices via Principal Component Pursuit

Cited by 72 publications

References 14 publications

Space-time signal processing for distributed pattern detection in sensor networks

Space-time signal processing for distributed pattern detection in sensor networks

An Improved Algorithm to Enhance Recovery Stability for Low-Rank Image

Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery

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