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Accession Number ADA586749
Title Robust Lasso with Missing and Grossly Corrupted Observations.
Publication Date Dec 2011
Media Count 11p
Personal Author N. H. Nguyen N. M. Nasrabadi T. D. Tran
Abstract This paper studies the problem of accurately recovering a sparse vector Beta* from highly corrupted linear measurements y = X Beta* + e* + w where e* is a sparse error vector whose nonzero entries may be unbounded and w is a bounded noise. We propose a so-called extended Lasso optimization which takes into consideration sparse prior information of both Beta* and e*. Our first result shows that the extended Lasso can faithfully recover both the regression and the corruption vectors. Our analysis is relied on a notion of extended restricted eigenvalue for the design matrix X. Our second set of results applies to a general class of Gaussian design matrix X with i.i.d rows N(0, Sigma), for which we provide a surprising phenomenon: the extended Lasso can recover exact signed supports of both Beta* and e* from only Omega (k log p log n) observations, even the fraction of corruption is arbitrarily close to one. Our analysis also shows that this amount of observations required to achieve exact signed support is optimal.
Keywords Optimization
Regression analysis
Robust lasso
Sparse noise
Sparse recovery
Sparse representation

Source Agency Non Paid ADAS
NTIS Subject Category 72F - Statistical Analysis
Corporate Author Johns Hopkins Univ., Baltimore, MD.
Document Type Technical report
Title Note Conference paper.
NTIS Issue Number 1405
Contract Number W911NF-11-1-0245

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