  The exact recovery property of Basis pursuit (BP) and Orthogonal Matching
Pursuit (OMP) has a relation with the coherence of the underlying frame. A
frame with low coherence provides better guarantees for exact recovery. In
particular, Incoherent Unit Norm Tight Frames (IUNTFs) play a significant role
in sparse representations. IUNTFs with special structure, in particular those
given by a union of several orthonormal bases, are known to satisfy better
theoretical guarantees for recovering sparse signals. In the present work, we
propose to construct structured IUNTFs consisting of large number of
orthonormal bases. For a given $r, k, m$ with $k$ being less than or equal to
the smallest prime power factor of $m$ and $r<k,$ we construct a CS matrix of
size $mk \times (mk\times m^{r})$ with coherence at most $\frac{r}{k},$ which
consists of $m^{r}$ number of orthonormal bases and with density $\frac{1}{m}$.
We also present numerical results of recovery performance of union of
orthonormal bases as against their Gaussian counterparts.
