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Collimators used to record gamma rays and neutrons from a nuclear test. In X-ray optics, gamma ray optics, and neutron optics, a collimator is a device that filters a stream of rays so that only those traveling parallel to a specified direction are allowed through. Collimators are used for X-ray, gamma-ray, and neutron imaging because it is ...
The algebraic reconstruction technique ( ART) is an iterative reconstruction technique used in computed tomography. It reconstructs an image from a series of angular projections (a sinogram ). Gordon, Bender and Herman first showed its use in image reconstruction; [1] whereas the method is known as Kaczmarz method in numerical linear algebra.
External beam radiation therapy ( EBRT) is a form of radiotherapy that utilizes a high-energy collimated beam of ionizing radiation, from a source outside the body, to target and kill cancer cells. A radiotherapy beam is composed of particles which travel in a consistent direction; each radiotherapy beam consists of one type of particle ...
An X-ray filter (or compensating filter) is a device placed in front of an X-ray source in order to reduce the intensity of particular wavelengths from its spectrum and selectively alter the distribution of X-ray wavelengths within a given beam before reaching the image receptor. [ 1] Adding a filtration device to certain x-ray examinations ...
The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [ 1] [ 2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such ...
Gauss–Seidel method. In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel.
Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where ...
General statement of the inverse problem. The inverse problem is the "inverse" of the forward problem: instead of determining the data produced by particular model parameters, we want to determine the model parameters that produce the data that is the observation we have recorded (the subscript obs stands for observed).