A compressive sensing approach for synthetic aperture imaging radiometers

The aperture synthesis technology represents a promising new approach to microwave radiometers for high-resolution observations of the Earth from geostationary orbit. However, the future application of the new technology may be limited by its large number of antennas, receivers, and correlators. In order to reduce significantly the complexity of the on-board hardware requirements, a novel method based on the recently developed theory of compressive sensing (CS) is proposed in this paper. Due to the fact that the brightness temperature distributions of the Earth have a sparse representation in some proper transform domain - for example, in terms of spatial finite-differences or their wavelet coefficients, we use the CS approach to significantly undersample the visibility function. Thus the number of antennas, receivers, and correlators can be further reduced than those based on the traditional methods that obey the Shannon/Nyquist sampling theorem. The reconstruction is performed by minimizing the ℓ₁ norm of a transformed image. The effectiveness of the proposed approach is validated by numerical simulations using the image corresponding to AMSU-A over the Pacific.