Theoretical Analysis of Compressive Sensing via Random Filter

Details Theoretical Analysis of Compressive Sensing via Random Filter Theoretical Analysis of Compressive Sensing via Random Filter

2008-11-02

arxiv.org/abs/0811.0152v1

Computer Science

Information Theory

Scientific paper

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.

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