Physical problems of computerized tomography

A cross-sectional image of an object can be accurately reconstructed if its projections or line integrals are known at all angles. This fundamental and exciting property has been applied to a variety of applications, primarily in the area of medical imaging. In many cases, however, the physical measurements fail to accurately define the complete set of line integrals. This leads to inaccuracies and distortions in the resultant reconstruction. The physical measurements can be inadequate in a number of ways. These include nonlinearities, noise, and insufficient data. The nonlinearities can arise from a nonlinear detector process, or the inability to accurately extract the information in the exponent by taking logs. The noise can be the usual statistical uncertainty of the measurement or an interfering component such as scatter. The data can be insufficient in a number of ways including inadequate sampling or regions of missing data. Also, the measurements of a source distribution can be distorted by an unknown attenuation distribution, resulting in errors in the reconstruction.