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Modern radar signal processing techniques make strong use of compressed sensing, affine rank minimization, and robust principle component analysis. The corresponding reconstruction algorithms should fulfill the following desired properties: complex valued, viable in the sense of not requiring parameters that are unknown in practice, fast convergence, low computational complexity, and high reconstruction performance. Although a plethora of reconstruction algorithms are available in the literature, these generally do not meet all of the aforementioned desired properties together. In this paper, a set of algorithms fulfilling these conditions is presented. The desired requirements are met by a combination of turbo-message-passing algorithms and smoothed ℓ0-refinements. Their performance is evaluated by use of extensive numerical simulations and compared with popular conventional algorithms.

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