A microwave imaging algorithm based on contrast-field equations is developed for sparse domains. The proposed algorithm is inspired by machine learning optimization schemes. More specifically it is based on Adam approach which is a first-order gradient optimization algorithm that has been studied intensively in optimizing artificial neural networks. To enforce sparsity constraint, the permittivity contrast at each iteration is subjected to a projection operator. The proposed algorithm has faster convergence than another state of art steepest descent approach used for microwave Imaging.