Landweber method in Hilbert and Banach spaces to reconstruct the NRCS field from GNSS-R measurements

In this study, reconstruction of the normalized radar cross-section (NRCS) image from noisy Global Navigation Satellite System Reflectometry (GNSS-R) Delay-Doppler Maps (DDMs) is addressed in both Hilbert and Banach spaces. The proposed approach, which is based on the Landweber regularization method, appropriately specialized to account for spatial invariance, is first developed in Hilbert space and then extended to the Banach space. The reconstruction performance of the methods is discussed using simulated DDMs and contrasted with a deconvolution technique based on constrained least squares (CLS). Experimental results demonstrate that the Landweber method in Banach space outperforms the Landweber method in Hilbert space and the CLS. In fact, these latter methods exhibit both over-smoothing and typical Gibbs-related oscillations.