Stabilized image reconstruction algorithm for Synthetic Aperture Imaging Radiometers.
Synthetic Aperture Imaging Radiometers (SAIR) promise to be powerful sensors for high-resolution observations of the Earth at low microwaves frequencies. The SMOS (Soil Moisture and Ocean Salinity) space mission is an ESA (European Space Agency) led project aimed at global monitoring of surface soil moisture and sea surface salinity from L-band space borne observations. It will be the first attempt to apply to remote sensing of the Earth surface, the concept of imaging interferometric radiometry by aperture synthesis, initially developed for radio astronomy. Interferometer measurements, also called complex visibilities, are obtained by cross-correlating the signals collected by pairs of spatially separated antennae which have overlapping fields of view. Visibility samples are related to the radiometric brightness temperature of the observed scene by a spatial Fourier-like integral. However, due to the angular extent of the target, the conditions, which typically apply for radio astronomy observations, are no longer valid for Earth remote sensing. As a consequence, the standard imaging algorithms developed by radio astronomers are not convenient for retrieving brightness temperatures of the scene from complex visibilities. The finite physical size of a synthetic antenna results in a truncation of the visibility samples above a certain spatial frequency. The Y-shaped array, filled with equally spaced elements, selected for SMOS leads to complex visibilities sampled over a hexagonal grid inside a star-shaped window in the Fourier domain. The relationship between complex visibility samples and radiometric brightness temperature can thus be rephrased in the Fourier domain: the unknowns are the Fourier components of the scene brightness temperature. Thanks to spatial redundancies, the number of these Fourier components inside the star-shaped window is smaller than the number of visibility samples: the over-determined inverse problem has to be solved in the least-squares sense. This contribution extends the concept of "resolvant matrix" to the case of remote sensing of the Earth at low microwaves frequencies. The stability of the reconstruction process is studied in depth, including the influence of the modeling of the instrument on the propagation of errors. To support the theory and to illustrate the performances of this imaging method, in terms of accuracy and computational time, numerical simulations are presented within the frame of the SMOS project.
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