  The problem of compressing a real-valued sparse source using compressive
sensing techniques is studied. The rate distortion optimality of a coding
scheme in which compressively sensed signals are quantized and then
reconstructed is established when the reconstruction is also required to be
sparse. The result holds in general when the distortion constraint is on the
expected $p$-norm of error between the source and the reconstruction. A new
restricted isometry like property is introduced for this purpose and the
existence of matrices that satisfy this property is shown.
