Abstract: Methods and systems for computed tomography provide advances in efficiency. The methods operating within the parallel-beam geometry, rather than a divergent beam geometry, for the majority of the operations. In back projection methods perform digital image coordinate transformations on selected intermediate-images, the parameters of one or more coordinate transformations being chosen such that Fourier spectral support of the intermediate-image is modified so that a region of interest has an increased extent along one or more coordinate direction and the aggregates of the intermediate-images can be represented with a desired accuracy by sparse samples.

Abstract: Methods and systems for computed tomography. A subject is imaged with a divergent beam source using a plurality of source positions and a detector array comprising a plurality of detector bins to obtain a representation of the subject including a plurality of image voxels. Contribution of a voxel to a detector bin in a computed forward projection or a detector bin to a voxel in a backprojection is determined by the intensity value assigned to the voxel, or to the detector bin, respectively, multiplied by the product of an area or volume of overlap and an additional weighting factor, and the area or volume of overlap is determined by overlap of the voxel with the area or volume of the image illuminated by a ray-wedge defined by detector bin edge rays.

Abstract: Methods and systems for iterative computed tomography add an auxiliary variable to the reconstruction process, while retaining all variables in the original formulation, A weighting operator or filter can be applied that causes the Hessian with respect to an image of the cost function to be well-conditioned. An auxiliary sinogram variable distinct from both a set of actual image measurements and from the set of projections computed based on an image can be applied to iteratively update during the statistical iterative image reconstruction, with applied conditions that causes the Hessian with respect to an image of the cost function to be well-conditioned.