STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION

doi:10.1016/S0252-9602(16)30101-1

Abstract

Abstract:

This paper establishes a high order condition on the restricted isometry property adapted to a frame D (D-RIP) for the signal recovery. It is shown that if the measurement matrix A satisfies the D-RIP condition δ_tk<√(t-1)/(t) for t>1, then all signals f which are sparse in terms of a tight frame D can be recovered stably or exactly via the l₁-analysis model based on y=Af+z in l₂ and Dantzig selector bounded noise setting.

Key words: compressed sensing, D-restricted isometry property, tight frame

CLC Number:

94A12

Wengu CHEN, Yaling LI. STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION[J].Acta mathematica scientia,Series B, 2016, 36(6): 1721-1730.

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