Computerized Tomography

Tomography refers to the synthesis of sectional images or slices from external measurements of a spatially varying function. Line integrals are the most common external measures, which are also known as projections. Availability of multiple projections at diierent orientations allows accurate recovery of the originating function. Because practical implementation of tomography typically requires large amounts of data and calculations, modern computing technologies are important. Computerized tomography (CT) is interdisciplinary, involving electrical and electronics engineering, mathematics, computer science, physics, mechanics and biomedical sciences. CT applications are numerous and diverse. Due to its penetrating power and contrast mechanism , X-ray CT has found wide use in medical imaging, industrial nondestructive evaluation, airport screening, and microtomography. In nuclear medicine, a radiating source distribution inside a patient is observed as the intensity of singly (single photon emission computerized tomography, SPECT) or pairwise (positron emission tomography, PET) emitted photons detected outside the patient. If the attenuation of the body is neglected, measures are line integrals of the source distribution. In magnetic resonance imaging (MRI), radio frequency electromagnetic waves are generated by changes of orientation and magnitude of internal magnetic elds, which are produced by spinning nuclei in external magnetic elds. The radio signals are detected by an antenna to provide information on the Fourier transform of a cross-section, which is directly related to line integrals of the nuclei density. In transmission electron microscopy, an electron beam penetrates a specimen over a limited angular range to collect projections. In ionospheric tomography, the total electron content is measured between an orbiting satellite and several ground stations. In geophysics, phase shifts of electromagnetic signals are detected for spatial reconstruction of the electrical conductivity and dielectric permittivity of the subsurface. In oceanography, acoustic transmission from a single source suspended from a ship to sonobuoys dropped from the air are recorded for mapping of ocean sound speed. In astronomy, the sun can be observed using an antenna with a parabolic section, and an integral signal is recorded over a thin strip of the radio emission distribution. By moving the antenna, the integrals are obtained over diierent strips for reconstruction of the radio emission distribution. CT principles are also applied in optical tomography, diiraction tomography, and 1