  The study of the restricted isometry property (RIP) of corrupted random
matrices is particularly important in the field of compressed sensing (CS) with
corruptions. If a matrix still satisfies the RIP after that a certain portion
of rows are erased, then we say that this matrix has the strong restricted
isometry property (SRIP). In the field of compressed sensing, random matrices
which satisfy certain moment conditions are of particular interest. Among these
matrices, those with entries generated from i.i.d. Gaussian or symmetric
Bernoulli random variables are often typically considered. Recent studies have
shown that matrices with entries generated from i.i.d. Gaussian random
variables satisfy the SRIP under arbitrary erasure of rows with high
probability. In this paper, we study the erasure robustness property of
Bernoulli random matrices. Our main result shows that with overwhelming
probability, the SRIP holds for Bernoulli random matrices. Moreover, our
analysis leads to a robust version of the famous Johnson-Lindenstrauss lemma
for Bernoulli random matrices.
