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Consistent and inconsistent equations. In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as ...
Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of ...
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 ...
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 ...
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.
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions for a system of linear equations, given the rank of its augmented matrix and coefficient matrix. The theorem is variously known as the: Rouché–Capelli theorem in English speaking countries, Italy and Brazil; Kronecker–Capelli theorem in Austria ...
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 ...
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 ...