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Synthetic aperture imaging radiometers (SAIRs) are potential powerful instruments for high-resolution observation of planetary surfaces at low microwave frequencies. This paper deals with the reconstruction of radiometric brightness temperature maps from SAIR interferometric measurements. It is demonstrated that the corresponding inverse problem is not well-posed and must, therefore, be regularized in order to provide a unique and stable solution. A new approach is presented by referring to the notion of modeling operator and to the concept of a resolving matrix of the instrument. To illustrate the theory, numerical simulations are carried out in reference to the Soil Moisture and Ocean Salinity space mission led by the European Space Agency. The results are discussed with emphasis on stability and error analysis.