L&lt;inf&gt;1&lt;/inf&gt;-fusion: Robust linear-time image recovery from few severely corrupted copies

Markopoulos, Panos P.; Kundu, Sandipan; Pados, Dimitris A.

doi:10.1109/icip.2015.7350995

Cited by 16 publications

(3 citation statements)

References 24 publications

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“…negative) definite because V 1 and V 2 are both positive definite. In this case, the L1-uLDA solution ( 24)-( 25) is a particular instance of LDA classifier (6) with generalized covariance (11). The only additional requirement for (24) to define an LDA solution is that δ = 0, which, according to Eqns.…”

Section: Link With Ldamentioning

confidence: 99%

LDA via L1-PCA of Whitened Data

Martı́n-Clemente

Zarzoso

2020

IEEE Trans. Signal Process.

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Principal component analysis (PCA) and Fisher's linear discriminant analysis (LDA) are widespread techniques in data analysis and pattern recognition. Recently, the L1-norm has been proposed as an alternative criterion to classical L2-norm in PCA, drawing considerable research interest on account of its increased robustness to outliers. The present work proves that, combined with a whitening preprocessing step, L1-PCA can perform LDA in an unsupervised manner, i.e., sparing the need for labelled data. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A number of numerical experiments on synthetic as well as real data confirm the theoretical findings.

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Section: Link With Ldamentioning

confidence: 99%

LDA via L1-PCA of Whitened Data

Martı́n-Clemente

Zarzoso

2020

IEEE Trans. Signal Process.

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“…Recently, Markopoulos et al [47,48] calculated optimally the maximum-projection L1-PCs of real-valued data, for which up to that point only suboptimal approximations were known [36][37][38]. Experimental studies in [47][48][49][50][51][52][53] demonstrated the sturdy resistance of optimal L1-norm principal-component analysis (L1-PCA) against outliers, in various signal processing applications. Recently, [43,45] introduced a heuristic algorithm for L1-PCA that was shown to attain state-of-the-art performance/cost trade-off.…”

Section: Introductionmentioning

confidence: 99%

Realified L1-PCA for direction-of-arrival estimation: theory and algorithms

Markopoulos

Tsagkarakis

Pados

et al. 2019

EURASIP J. Adv. Signal Process.

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Subspace-based direction-of-arrival (DoA) estimation commonly relies on the Principal-Component Analysis (PCA) of the sensor-array recorded snapshots. Therefore, it naturally inherits the sensitivity of PCA against outliers that may exist among the collected snapshots (e.g., due to unexpected directional jamming). In this work, we present DoA-estimation based on outlier-resistant L1-norm principal component analysis (L1-PCA) of the realified snapshots and a complete algorithmic/theoretical framework for L1-PCA of complex data through realification. Our numerical studies illustrate that the proposed DoA estimation method exhibits (i) similar performance to the conventional L2-PCA-based method, when the processed snapshots are nominal/clean, and (ii) significantly superior performance when the snapshots are faulty/corrupted.

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“…The same sensitivity has also been documented in PCA, which is a special case of Tucker for 2-way tensors (matrices). For matrix decomposition, L1-norm-based PCA (L1-PCA) [21], formulated by simple substitution of the L2-norm in PCA with the L1-norm, has exhibited solid robustness against heavily corrupted data in an array of applications [22]- [24]. Similar outlier resistance has been recently attained by algorithms for L1-norm reformulation of Tucker2 decomposition of 3-way tensors (L1-Tucker2) [20], [25]- [27].…”

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confidence: 99%

L1-Norm Tucker Tensor Decomposition

2019

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Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries.In this work, we explore L1-Tucker, an L1-norm based reformulation of standard Tucker decomposition. After formulating the problem, we present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The presented algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker, implemented by means of the proposed methods, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.

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L<inf>1</inf>-fusion: Robust linear-time image recovery from few severely corrupted copies

Cited by 16 publications

References 24 publications

LDA via L1-PCA of Whitened Data

LDA via L1-PCA of Whitened Data

Realified L1-PCA for direction-of-arrival estimation: theory and algorithms

L1-Norm Tucker Tensor Decomposition

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