Systems and methods are provided which utilize a fast, efficient filtered backprojection algorithm that can provide noise suppression advantages of an iterative MAP reconstruction algorithm. In some embodiments novel filtered backprojection systems are able to provide an image which emulates an image from an iterative algorithm corresponding to a selected iteration by utilizing control parameters which shape the filter accordingly during the reconstruction process. For example, if a user desires an image which would correspond to the one-hundredth iteration of an iterative algorithm, embodiments can provide a similar quality image using minimal calculation steps. Further, embodiments may provide the resolution quality of such an iteration while also allowing for better shift-invariant performance than an iterative method.