Stable recovery of signals with the high order D-rip Condition

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 δtk < 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.