An Adaptive $L^{p}$ -Penalization Method to Enhance the Spatial Resolution of Microwave Radiometer Measurements

Abstract

In this paper, we introduce a novel approach to enhance the spatial resolution of single-pass microwave data collected by mesoscale sensors. The proposed rationale is based on an $L^{p}$ -minimization approach with a variable $p$ exponent. The algorithm automatically adapts the $p$ exponent to the region of the image to be reconstructed. This approach allows taking benefit of the advantages of both the regularization in Hilbert ( $p = 2$ ) and Banach ( $1 ) spaces. Experiments are undertaken considering the microwave radiometer and refer to both actual and simulated data collected by the special sensor microwave imager (SSM/I). Results demonstrate the benefits of the proposed method in reconstructing abrupt discontinuities and smooth gradients with respect to conventional approaches in Hilbert or Banach spaces.