Compressive Sampling via Random Convolution

Several recent results in compressive sampling show that a sparse signal (i.e. a signal which can be compressed in a known orthobasis) can be efficiently acquired by taking linear measurements against random test functions. In this paper, we show that these results can be extended to measurements taken by convolving with a random pulse and then subsampling. The measurement scheme is universal in that it complements (with high probability) any fixed orthobasis we use to represent the signal. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)