SURE-Based Regularization Parameter Selection for TomoSAR Imaging via Maximum-Likelihood

Abstract

Regularized iterative reconstruction algorithms for Synthetic Aperture Radar (SAR) Tomography (TomoSAR), like the ones based on Maximum Likelihood (ML), offer an accurate estimate of the Power Spectrum Pattern (PSP) displaced along the Perpendicular to the Line-of-Sight (PLOS) direction. The recovered PSP is considered as ‘good-fitted’ or ‘appropriate-fitted’, since the reconstruction fits correctly enough with the position and density of the objectives in the field backscattered towards the sensor. However, the correct functioning of these regularization approaches is constrained to the proper selection of the regularization parameters. Therefore, for such a purpose, this paper suggests using a criterion based on the Stein’s Unbiased Risk Estimate (SURE) strategy. SURE approximates the Mean Square Error (MSE) between the estimated and actual PSP, purely from the measured (observed) data, without the need of any knowledge about the true PSP. Consequently, the proper selection of the regularization parameters corresponds to the minimum SURE value, which guarantees having a ‘good-fitted’ reconstruction. The experiments are performed in simulated data for different representative cases.