  The purpose of this note is to establish a new generalized
Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for
compressed sensing.
  For fulfilling D-RIP, the constant $\delta_k$ is used in the definition: $(1
-\delta_k)\|D v\|_2^2 \le \|\Phi D v\|_2^2 \le (1 + \delta_k)\|D v\|^2$. We
prove that signals with $k$-sparse $D$-representation can be reconstructed if
$\delta_{2k} < \frac{2}3$.
  The approach in this note can be extended to obtain other D-RIP bounds (i.e.,
$\delta_{tk}$).
