Geometric tomography: A limited-view approach for computed tomography

Computed tomography(CT), especially since the introduction of helical CT, provides excellent visualization of the internal organs of the body. As a result, CT is used routinely in the clinical arena to obtain three- and four-dimensional data. Data is obtained by exposing patients to a beam of x-rays from a number (about 1000) of different angles (projections). Then, standard CT makes use of the Radon transform to generate 3D data, denoted f→, directly from projections, denoted g→. Thus, the projection relationship can be represented in matrix form by g→ = M f→ where M represents the projection matrix. Note that techniques based on the Radon transform are in general limited by the Nyquist sampling criteria. The increasing use of CT has resulted in a substantial rise in population-radiation-dose [1], which may lead to an increased incidence of cancer in the population. In addition to increased use, the number of projections in the CT acquisitions is increasing to improve image quality which further increases patient radiation exposure as well as the reconstruction time. This latter issue can be improved by using new technology, e.g., graphical processing units (GPUs) [2], but the problem of radiation dose does remains. Reduction of the number of projections can result in artifacts and reduced image quality. Thus, new approaches are being pursued.