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In MIMO Radar schemes, sparse scenarios have been successfully exploited by compressed sensing (CS) techniques. We address the ill-conditioning inherent to the linear model of a 3D Radar imaging system, by proposing a two-step decoupling procedure which induces structure, and allows for fast matrix products to efficiently recover the target image. This is accomplished by further combining it with an Approximate Message Passing algorithm, that yields two iterative versions for range and cross-range image recovery. Simulations suggest that besides computational efficiency, decoupling the full model matrix gives us more freedom in selecting the CS regularization levels. An FDTD based experiment also shows that the algorithms are robust in real life situations where nonideal antennas and multiple scattering naturally occur.