  In this paper, the theoretical analysis of compressive sensing via random
filter, firstly outlined by J. Romberg [compressive sensing by random
convolution, submitted to SIAM Journal on Imaging Science on July 9, 2008], has
been refined or generalized to the design of general random filter used for
compressive sensing. This universal CS measurement consists of two parts: one
is from the convolution of unknown signal with a random waveform followed by
random time-domain subsampling; the other is from the directly time-domain
subsampling of the unknown signal. It has been shown that the proposed approach
is a universally efficient data acquisition strategy, which means that the
n-dimensional signal which is S sparse in any sparse representation can be
exactly recovered from Slogn measurements with overwhelming probability.
