  Near-field radar imaging systems are used in a wide range of applications
such as concealed weapon detection and medical diagnosis. In this paper, we
consider the problem of reconstructing the three-dimensional (3D)
complex-valued reflectivity distribution of the near-field scene by enforcing
regularization on its magnitude. We solve this inverse problem by using the
alternating direction method of multipliers (ADMM) framework. For this, we
provide a general expression for the proximal mapping associated with such
regularization functionals. This equivalently corresponds to the solution of a
complex-valued denoising problem which involves regularization on the
magnitude. By utilizing this expression, we develop a novel and efficient
plug-and-play (PnP) reconstruction method that consists of simple update steps.
Due to the success of data-adaptive deep priors in imaging, we also train a 3D
deep denoiser to exploit within the developed PnP framework. The effectiveness
of the developed approach is demonstrated for multiple-input multiple-output
(MIMO) imaging under various compressive and noisy observation scenarios using
both simulated and experimental data. The performance is also compared with the
commonly used direct inversion and sparsity-based reconstruction approaches.
The results demonstrate that the developed technique not only provides
state-of-the-art performance for 3D real-world targets, but also enables fast
computation. Our approach provides a unified general framework to effectively
handle arbitrary regularization on the magnitude of a complex-valued unknown
and is equally applicable to other radar image formation problems (including
SAR).
