Open AccessRestricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements
Author(s) -
Qingshan You,
Qun Wan,
Haiwen Xu
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/959403
Subject(s) - restricted isometry property , principal component analysis , robust principal component analysis , property (philosophy) , matrix (chemical analysis) , rank (graph theory) , isometry (riemannian geometry) , convex optimization , operator (biology) , component (thermodynamics) , mathematical optimization , regular polygon , mathematics , linear programming , matrix completion , compressed sensing , computer science , algorithm , combinatorics , artificial intelligence , pure mathematics , physics , geometry , philosophy , materials science , repressor , chemistry , composite material , biochemistry , epistemology , quantum mechanics , transcription factor , thermodynamics , gaussian , gene
The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP_RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming
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