  Compressed Sensing aims to capture attributes of a sparse signal using very
few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is
possible if the sensing matrix acts as a near isometry on all
$\boldsymbol{k}$-sparse signals. This property holds with overwhelming
probability if the entries of the matrix are generated by an iid Gaussian or
Bernoulli process. There has been significant recent interest in an alternative
signal processing framework; exploiting deterministic sensing matrices that
with overwhelming probability act as a near isometry on $\boldsymbol{k}$-sparse
vectors with uniformly random support, a geometric condition that is called the
Statistical Restricted Isometry Property or StRIP. This paper considers a
family of deterministic sensing matrices satisfying the StRIP that are based on
\srm codes (binary chirps) and a $\boldsymbol{k}$-sparse reconstruction
algorithm with sublinear complexity. In the presence of stochastic noise in the
data domain, this paper derives bounds on the $\boldsymbol{\ell_2}$ accuracy of
approximation in terms of the $\boldsymbol{\ell_2}$ norm of the measurement
noise and the accuracy of the best $\boldsymbol{k}$-sparse approximation, also
measured in the $\boldsymbol{\ell_2}$ norm. This type of $\boldsymbol{\ell_2
/\ell_2}$ bound is tighter than the standard $\boldsymbol{\ell_2 /\ell_1}$ or
$\boldsymbol{\ell_1/ \ell_1}$ bounds.
