New Bounds for RIC in Compressed Sensing

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 δ 8ak <1 and δₖ₊ₐₖ<3/2-1+√(4a+3)²-88a for a> 3/8 , then k-sparse solution can be recovered exactly via l 1 minimization in the noiseless case. In particular, when a=1,1.5,2 and 3, we have δ 2k <0.5746 and δ 8k <1, or δ 2.5k <0.7046 and δ 12k <1, or δ 3k <0.7731 and δ 16k <1 or δ 4k <0.8445 and δ 24k <1.