Proceedings of the Twenty-First Annual Hawaii International Conference on Applications Track
Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
Image Representation Via a Finite Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
DICTA '05 Proceedings of the Digital Image Computing on Techniques and Applications
The mojette transform: the first ten years
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Exact, scaled image rotation using the finite radon transform
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Exact, scaled image rotations in finite Radon transform space
Pattern Recognition Letters
Growth of discrete projection ghosts created by iteration
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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Mojette projections of discrete pixel arrays form good approximations to experimental parallel-beam x-ray intensity absorption profiles. They are discrete sums taken at angles defined by rational fractions. Mojette-like projections form a "half-way house" between a conventional sinogram and fully digital projection data. A new direct and exact image reconstruction technique is proposed here to invert arbitrary but sufficient sets of Mojette data. This new method does not require iterative, statistical solution methods, nor does it use the efficient but noise-sensitive "corner-based" inversion method. It instead exploits the exact invertibility of the prime-sized array Finite Radon Transform (FRT), and the fact that all Mojette projections can be mapped directly into FRT projections. The algorithm uses redundant or "calibrated" areas of an image to expand any asymmetric Mojette set into the smallest symmetric FRT set that contains all of the Mojette data without any re-binning. FRT data will be missing at all angles where Mojette data is not provided, but can be recovered exactly from the "ghost projections" that are generated by back-projecting all the known data across the calibrated regions of the reconstructed image space. Algorithms are presented to enable efficient image reconstruction from any exact Mojette projection set, with a view to extending this approach to invert real x-ray data.