Reconstruction algorithm
Encyclopedia
In tomography
, a variety of practical reconstruction algorithms have been developed to implement the process of reconstruction of a 3-dimensional object from its projections. These algorithms are designed largely based on the mathematics
of the Radon transform
, statistical knowledge of the data acquisition process and geometry of the data imaging system.
Tomography
Tomography refers to imaging by sections or sectioning, through the use of any kind of penetrating wave. A device used in tomography is called a tomograph, while the image produced is a tomogram. The method is used in radiology, archaeology, biology, geophysics, oceanography, materials science,...
, a variety of practical reconstruction algorithms have been developed to implement the process of reconstruction of a 3-dimensional object from its projections. These algorithms are designed largely based on the mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
of the Radon transform
Radon transform
thumb|right|Radon transform of the [[indicator function]] of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero.thumb|right|Original function is equal to one on the white region and zero on the dark region....
, statistical knowledge of the data acquisition process and geometry of the data imaging system.
See also
- Tomographic reconstructionTomographic reconstructionThe mathematical basis for tomographic imaging was laid down by Johann Radon. It is applied in computed tomography to obtain cross-sectional images of patients...
- Computed tomographyComputed tomographyX-ray computed tomography or Computer tomography , is a medical imaging method employing tomography created by computer processing...
- Positron emission tomographyPositron emission tomographyPositron emission tomography is nuclear medicine imaging technique that produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide , which is introduced into the body on a...
- SPECT
- Discrete tomographyDiscrete tomographyDiscrete Tomography focuses on the problem of reconstruction of binary images from a small number of their projections....