Optimal D-RIP bounds in compressed sensing

This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition . k < 1/3 or .2k<2../2, then all signals f with D*f are k-sparse can be recovered exactly via the constrained . 1 minimization based on y = Af, where D* is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang.s work. These bounds are greatly improved comparing to the condition . k < 0.307 or . 2k < 0.4931. Besides, if . k < 1/3 or .2k<2../2, the signals can also be stably reconstructed in the noisy cases.