Recent Advances in Matrix Completion Techniques as Applied to Tomographic Imaging

Innovative inversion methodologies exploiting the paradigm of Bayesian Compressive Sensing (BCS) have been successfully introduced in the last few years to address sparse and linear microwave imaging problems. Their success is motivated by several concurring factors, including their capability to estimate the 'confidence level' of the obtained inversions. Despite the informative content associated to such estimations, confidence maps have been mostly used to assess the quality of microwave images rather than to enhance it. The possibility to integrate rank-minimization techniques with BCS imaging strategies, recently introduced in the framework of Matrix Completion Inversion, will be reviewed in this work. Selected numerical examples considering a Born formulation of the tomographic microwave imaging problem will be presented to illustrate the features and capabilities of the arising techniques.