Abstract:

This paper gives new bounds for restricted isometry constant (RIC) in compressed
sensing. Let Φ be an 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
δ8ak < 1 and some other conditions
, 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 and
δ8k < 1, or δ2.5k < 0.7046 and δ12k < 1, or δ3k < 0.7731 and δ16k < 1 or δ4k < 0.8445
and δ24k < 1.