This paper presents a study investigating the reconstruction of cross sectional images of a time-varying object from its projections. Ideally, to obtain high quality cross sectional images of a time-varying object, the projections measured should correspond to that of the same phase of the object. This in turn requires that the projections from different projection angles be collected at a high rate—a requirement that is difficult to achieve for various practical reasons. In this paper, we use a priori knowledge of underlying object and the spectral properties of the projections to overcome the deficiency of inconsistent projections, and develop a novel image reconstruction method. Computer simulations demonstrate that the proposed method is capable of reducing the reconstruction mean squared error and generating reconstructions with much improved quality.