This paper improves bounds for restricted isometry constant (RIC) in compressed sensing. Let \phi be a m*n real matrix and k be a positive integer with k<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 \dalta_2k<0.5746; \dalta_2.5k<0.7074; \dalta_3k<0.7731 and \dalta_4k<0.8445, which are the best bounds for RIC to our knowledge.
July 30, 2012. Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China
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