Towards Omni-Tomography—Grand Fusion of Multiple Modalities for Simultaneous Interior Tomography

We recently elevated interior tomography from its origin in computed tomography (CT) to a general tomographic principle, and proved its validity for other tomographic modalities including SPECT, MRI, and others. Here we propose “omni-tomography”, a novel concept for the grand fusion of multiple tomographic modalities for simultaneous data acquisition in a region of interest (ROI). Omni-tomography can be instrumental when physiological processes under investigation are multi-dimensional, multi-scale, multi-temporal and multi-parametric. Both preclinical and clinical studies now depend on in vivo tomography, often requiring separate evaluations by different imaging modalities. Over the past decade, two approaches have been used for multimodality fusion: Software based image registration and hybrid scanners such as PET-CT, PET-MRI, and SPECT-CT among others. While there are intrinsic limitations with both approaches, the main obstacle to the seamless fusion of multiple imaging modalities has been the bulkiness of each individual imager and the conflict of their physical (especially spatial) requirements. To address this challenge, omni-tomography is now unveiled as an emerging direction for biomedical imaging and systems biomedicine

Local Tomography With Nonsmooth Attenuation

Local tomography for the Radon transform with nonsmooth attenuation is proposed and justified. The main theoretical tool is analysis of singularities of pseudodifferential operators with nonsmooth symbols. Results of numerical testing of local tomography are presented. ©1999 American Mathematical Society

Local tomography for the limited-angle problem

We investigate local tomography in the case of limited-angle data. The main theoretical tool is analysis of the singularities of pseudodifferential operators (PDO) acting on piecewise-smooth functions. Amplitudes of the PDO we consider are allowed to be nonsmooth in the dual variable ξ across the boundary of a wedge. Results of numerical simulation of limited-angle local tomography confirm basic theoretical conclusions. © 1997 Academic Press

Local tomography for the limited-angle problem

We investigate local tomography in the case of limited-angle data. The main theoretical tool is analysis of the singularities of pseudodifferential operators (PDO) acting on piecewise-smooth functions. Amplitudes of the PDO we consider are allowed to be nonsmooth in the dual variable ξ across the boundary of a wedge. Results of numerical simulation of limited-angle local tomography confirm basic theoretical conclusions. © 1997 Academic Press

Novel techniques for image computation and a concomitant reduction of the x-ray dose in transmission tomography

Conventional tomographic imaging techniques are nonlocal: to reconstruct an unknown function f at a point x, one needs to know its Radon transform (RT) {cflx f} ({theta},p). Suppose that one is interested in the recovery of f only for x in some set U. The author calls U the region of interest (ROI). Define the local data as the integrals of f along the lines that intersect the ROI. He proposes algorithms for finding locations and values of jumps (sharp variations) of f from only the local data. In case of transmission tomography, this results in a reduction of the x-ray dose to a patient. The proposed algorithms can also be used in emission tomographies. They allow one: to image jumps of f with better resolution than conventional techniques; to take into account variable attenuation (if it is known); and to obtain meaningful images even if the attenuation is not known. Results of testing the proposed algorithms on the simulated and real data are presented