Conjugate Gradient Method in Hilbert and Banach Spaces to Enhance the Spatial Resolution of Radiometer Data

In this paper, a new computer-time effective iterative method is proposed to enhance the spatial resolution of microwave radiometer data in both Hilbert and Banach spaces. The reconstruction method is based on the conjugate gradient (CG) method. CG is a well-known method in electromagnetics, where it is commonly used to address inverse problems in Hilbert spaces. However, the method has never been applied to inverse problems related to spatial resolution enhancement of microwave remotely sensed measurements. In this paper, CG is adapted to the microwave radiometer case and exploited to reconstruct the brightness field at enhanced spatial resolution. Then, CG is, for the first time, extended to Banach spaces by means of duality maps and then applied to enhance the radiometer spatial resolution. Experiments undertaken on both simulated and actual radiometer data confirm the soundness of the proposed approach in Banach spaces and demonstrate that CG is able to provide a reconstruction accuracy similar to the conventional Landweber method, but with a significantly reduced processing time.