  The aim of this paper is to discuss some advanced aspects of image
reconstruction in single-pixel cameras, focusing in particular on detectors in
the THz regime. We discuss the reconstruction problem from a computational
imaging perspective and provide a comparison of the effects of several
state-of-the art regularization techniques.
  Moreover, we focus on some advanced aspects arising in practice with THz
cameras, which lead to nonlinear reconstruction problems: the calibration of
the beam reminiscent of the Retinex problem in imaging and phase recovery
problems. Finally we provide an outlook to future challenges in the area.
