Neutron Computed Tomography (CT) is an increasingly utilised non-destructive analysis tool in material science, palaeontology, and cultural heritage. With the development of new neutron imaging facilities (such as DINGO, ANSTO, Australia) new opportunities arise to maximise their performance through the implementation of statistically driven image reconstruction methods which have yet to see wide scale application in neutron transmission tomography. This work outlines the implementation of a convex algorithm statistical image reconstruction framework applicable to the geometry of most neutron tomography instruments with the aim of obtaining similar imaging quality to conventional ramp filtered back-projection via the inverse Radon transform, but using a lower number of measured projections to increase object throughput. Through comparison of the output of these two frameworks using a tomographic scan of a known 3 material cylindrical phantom obtain with the DINGO neutron radiography instrument (ANSTO, Australia), this work illustrates the advantages of statistical image reconstruction techniques over conventional filter back-projection. It was found that the statistical image reconstruction framework was capable of obtaining image estimates of similar quality with respect to filtered back-projection using only 12.5% the number of projections, potentially increasing object throughput at neutron imaging facilities such as DINGO eight-fold.