  Structurally random matrices (SRMs) are a practical alternative to fully
random matrices (FRMs) when generating compressive sensing measurements because
of their computational efficiency and their universality with respect to the
sparsifing basis. In this work we derive the statistical distribution of
compressive measurements generated by various types of SRMs, as a function of
the signal properties. We show that under a wide range of conditions, that
distribution is a mixture of asymptotically multi-variate normal components. We
point out the implications for quantization and coding of the measurements and
discuss design consideration for measurements transmission systems. Simulations
on real-world video signals confirm the theoretical findings and show that the
signal randomization of SRMs yields a dramatic improvement in quantization
properties.
