Microwave Imaging Within the First-Order Born Approximation by Means of the Contrast-Field Bayesian Compressive Sensing

A new approach based the contrast field (CF) formulation of the microwave imaging problem that exploits the Bayesian compressive sampling (BCS) paradigm is proposed for the reconstruction of sparse distributions of weak scatterers. Towards this end, the original inverse scattering problem is recast to a probabilistic sparseness constrained optimization by introducing suitable hierarchical priors as sparsity constraints. A fast relevance vector machine (RVM) is then employed to reconstruct the scatterers as well as to estimate the “confidence level” of the inversion. Representative numerical results are presented to illustrate the method as well as to assess its potentialities and limitations in terms of inversion accuracy, computational efficiency, and robustness. Comparisons with state-of-the-art deterministic and stochastic reconstruction methodologies still within the Born approximation (BA) are discussed, as well.