Iterative Sparse Maximum Likelihood-based ...

This paper presents a series of iterative sparse maximum likelihood-based approaches (SMLA) with applications to synthetic aperture radar (SAR) imaging. By using a particular form of Gaussian signal prior, iterative analytical expressions of the signal and noise power estimates are obtained by iteratively minimizing the stochastic maximum likelihood (SML) function with respect to only one scalar parameter at a time, resulting in power-based SMLA approaches. However, these power-based sparse approaches do not provide the phases of the unknown signals. To address this problem, a combined SMLA and Maximum A Posteriori (MAP) approach (referred to as the SMLA-MAP approach) for estimating the unknown complex-valued signals is proposed. The SMLA-MAP derivation is inspired by the sparse learning via iterative minimization (SLIM) approach, where a modified expression of the SLIM noise power estimation is proposed. We also show that SLIM can be viewed as a combination of the deterministic ML (DML) and iteratively re-weighted least squares (IRLS) approaches. Finally, numerical examples of SAR imaging using Slicy data, Backhoe data and Gotcha data are generated to compare the performances of the proposed and existing approaches?.