Algebraic Reconstruction Technique
Encyclopedia
Sinogram
Sinogram can mean,* a Chinese character even when used in a different language, such as Japanese , Korean or Vietnamese* a tetragram which follows the graphic conventions of Chinese characters, e.g...
), used in computed tomography
Computed tomography
X-ray computed tomography or Computer tomography , is a medical imaging method employing tomography created by computer processing...
. For image reconstruction it was introduced in , while in numerical linear algebra the method is known as Kaczmarz method
Kaczmarz method
The Kaczmarz method, based on the work of the Polishmathematican Stefan Kaczmarz,is a method for solving linear systems of equations A x = b .It was rediscovered in the field of image reconstruction from projections by...
.
In fact, ART can be considered as an iterative solver of a system of linear equations (the values of the pixels are considered as variables collected in a vector
, the image process is described by a matrix 
, and the measured angular projects are collected in a vector 
). Given a real or complex
matrix
and a real or complex vector
,respectively, the method computes an approximation of the solution of the linear
systems of equations as in the following formula,
-
where
,
is the i-th row of the matrix
,
is the i-th component of the vector
,
and
is a relaxation parameter. The above formulae gives a simple iteration routine.
An advantage of ART over other reconstruction methods (such as filtered backprojection) is that it is relatively easy to incorporate prior knowledge into the reconstruction process.
For further details see Kaczmarz methodKaczmarz methodThe Kaczmarz method, based on the work of the Polishmathematican Stefan Kaczmarz,is a method for solving linear systems of equations A x = b .It was rediscovered in the field of image reconstruction from projections by...
.