Improved bounds on restricted isometry constant for orthogonal matching pursuit

First, a counter example is constructed to show that for any given positive integer K >= 2 and for any (1/root K + 1) <= t < 1, there always exists a K- sparse x and a matrix A with the restricted isometry constant delta(K+1) = t such that the orthogonal matching pursuit (OMP) algorithm fails in K iterations. Secondly, it is shown that even when delta(K+1) = (1/(root K + 1)), the OMP algorithm can also perfectly recover every K- sparse vector x from y = Ax in K iterations. This improves the best existing results which were independently given by Mo and Shen and Wang and Shim.