The limitations in neutron flux and resolution (1/D) of current neutron imaging systems can be addressed with a Coded Source Imaging system with magnification (xCSI). More precisely, the multiple sources in an xCSI system can exceed the flux of a single pinhole system for several orders of magnitude, while maintaining a higher 1 / D with the small sources. Moreover, designing for an xCSI system reduces noise from neutron scattering, because the object is placed away from the detector to achieve magnification. However, xCSI systems are adversely affected by correlated noise such as non-uniform illumination of the neutron source, incorrect sampling of the coded radiograph, misalignment of the coded masks, mask transparency, and the imperfection of the system Point Spread Function (PSF). We argue that a model-based reconstruction algorithm can overcome these problems and describe the implementation of a Simultaneous Iterative Reconstruction Technique algorithm for coded sources. Design pitfalls that preclude a satisfactory reconstruction are documented.