  Compressed sensing was proposed by E. J. Cand\'es, J. Romberg, T. Tao, and D.
Donoho for efficient sampling of sparse signals in 2006 and has vast
applications in signal processing. The expicit restricted isometry property
(RIP) measurement matrices are needed in practice. Since 2007 R. DeVore, J.
Bourgain et al and R. Calderbank et al have given several deterministic
cosntrcutions of RIP matrices from various mathematical objects. On the other
hand the strong coherence property of a measurement matrix was introduced by
Bajwa and Calderbank et al for the recovery of signals under the noisy
measuremnt. In this paper we propose new explicit construction of real valued
RIP measurement matrices in compressed sensing from algebraic geometry. Our
construction indicates that using more general algebraic-geometric objects
rather than curves (AG codes), RIP measurement matrices in compressed sensing
can be constructed with much smaller coherence and much bigger sparsity orders.
The RIP matrices from algebraic geometry also have a nice asymptotic bound
matching the bound from the previous constructions of Bourgain et al and the
small-bias sets. On the negative side, we prove that the RIP matrices from
DeVore's construction, its direct algebraic geometric generalization and one of
our new construction do not satisfy the strong coherence property. However we
give a modified version of AG-RIP matrices which satisfies the strong coherence
property. Therefore the new RIP matrices in compressed sensing from our
modified algebraic geometric construction can be used for the recovery of
signals from the noisy measurement.
