Reduction of the Instrument Model Error in Aperture Synthesis Radiometers

Aperture synthesis radiometers measure the visibilities of the scene under observation by an antenna array, and based on these visibility measurements, inverse algorithm is employed to reconstruct the brightness temperature of the observed scene. The instrument model plays a key role in the inverse problem and its error will degrade the reconstruction accuracy. This work provides an analysis of the impact of the instrument model error on the reconstruction accuracy and a method regarding how to reduce its impact. It will be demonstrated in this work that the point spread functions (PSFs) of the imaging system at different spatial locations are highly correlated with each other, but the PSF errors are not. Benefit from this fact, the PSF can be represented as a sum of basis functions obtained from principal component analysis of PSF. It can be observed that most of the energy of the true PSF is concentrated on the first L principal components, and the last N-L principal components can be neglected due to that they are dominated by the noise. Numerical studies are carried out using the data obtained from the Soil Moisture and Ocean Salinity (SMOS) official website, and the corresponding results validate that the proposed method is effective in reducing the instrument model error.