(c) British Crown Copyright 2018/AWE In this study we explore the feasibility of reconstructing the density distribution of a cargo container to an appropriate degree using gravity gradiometry with the aim of identifying the presence of fissile material. The resulting inverse problem is highly ill-posed with a large null space and so several techniques are used to attempt to achieve accurate and reliable solutions. A level set method is employed to model the sharp discontinuities expected, built on the use of radial basis functions. Local and global optimisation methods are explored, including sparsity, gradient descent and a genetic algorithm. Ultimately two optimisation methods, the method of steepest descent and a genetic algorithm, are combined in an ensemble hybrid algorithm that utilises information obtained about the eccentricities of this particular problem to produce many solutions. The solutions are analysed in an effort to provide an indicator for the presence of high density material whilst avoiding both false positive and negative results.