Neutron Computed Tomography (CT) is a widely utilised non-destructive analysis tool within the fields of 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 the field. This work outlines the implementation of a convex algorithm statistical image reconstruction framework applicable to the geometry of most neutron CT beamlines 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. These two frameworks were applied to a tomographic scan of a known phantom obtained with the neutron radiography instrument DINGO at the OPAL research reactor (ANSTO, Australia) and their recovered object reconstructions compared. 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.