Improved Bounds for RIC in Compressed Sensing

This paper improves bounds for restricted isometry constant (RIC) in compressed sensing. Let Φ be a m × n real matrix and k be a positive integer with k ≤ n. The main results of this paper show that if the restricted isometry constant of Φ satisfies δk+ak < 3 2 − 1 + √ (4a+ 3)2 − 8 8a for a > 3 8 , then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case. In particular, when a = 1, 1.5, 2 and 3, we have δ2k < 0.5746, δ2.5k < 0.7074∗, δ3k < 0.7731 and δ4k < 0.8445, which are the best bounds for RIC to our knowledge.