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 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: Pixel images {circumflex over (f)} are created from projections (q1 . . . qp) by backprojecting selected projections to produce intermediate images (Il,m), and performing digital image coordinate transformations and/or resampling on selected intermediate images. The digital image coordinate transformations are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets, and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image {circumflex over (f)}. Digital image coordinate transformation can include rotation, shearing, stretching, contractions. Resampling can include up-sampling, down-sampling, and the like.

Abstract: Pixel images f are created from projections (q1 . . . qp) by backprojecting (100) selected projections to produce intermediate images (I1, m), and performing digital image coordinate transformations (102) and/or resampling (FIG. 31, 186, 192, 196) on selected intermediate images. The digital image coordinate transformations (102) are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets (104), and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image f. Digital image coordinate transformation can include rotation (FIG. 18, 102), shearing (FIG. 10B, 120, 122), stretching, contractions (109), etc. Resampling can include up-sampling (101, 106), down-sampling (109), and the like.

Abstract: Pixel images {circumflex over (f)} are created from projections (q1 . . . qp) by backprojecting selected projections to produce intermediate images (Il,m), and performing digital image coordinate transformations and/or resampling on selected intermediate images. The digital image coordinate transformations are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets, and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image {circumflex over (f)}. Digital image coordinate transformation can include rotation, shearing, stretching, contractions. Resampling can include up-sampling, down-sampling, and the like.