Sampling by blocks of measurements in compressed sensing

Abstract

Various acquisition devices impose sampling blocks of measurements. A typical example is parallel magnetic resonance imaging (MRI) where several radio-frequency coils simultaneously acquire a set of Fourier modulated coefficients. We study a new random sampling approach that consists in selecting a set of blocks that are predefined by the application of interest. We provide theoretical results on the number of blocks that are required for exact sparse signal reconstruction. We finish by illustrating these results on various examples, and discuss their connection to the literature on CS.