Multi-channel reconstruction from a randomly sampled array

Compressive sampling has a rich theoretical background in a number of fields from image processing to medical imaging to geophysical data analysis. In this paper we explore compressive sampling from the perspective of classic array processing. We derive a basis appropriate for reconstructing multichannel data which is sparsely sampled from a uniform linear array. Here we reconstruct both time and spatial components of the signal using randomly sampled time series. We present both theoretical and experimental evidence that compressive sampling can be successful for traditional array processing applications.