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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.
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 ...
It is so called because the impulse response is matched to input pulse signals. Two-dimensional matched filters are commonly used in image processing, e.g., to improve the SNR of X-ray observations. Matched filtering is a demodulation technique with LTI (linear time invariant) filters to maximize SNR. [3] It was originally also known as a North ...
Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method . We seek the solution to a set of linear equations, expressed in matrix terms as. The Richardson iteration is.
Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.
A passive phased array or passive electronically scanned array (PESA) is a phased array in which the antenna elements are connected to a single transmitter and/or receiver, as shown in the first animation at top. PESAs are the most common type of phased array. Generally speaking, a PESA uses one receiver/exciter for the entire array.
Adaptive filter. An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm. Because of the complexity of the optimization algorithms, almost all adaptive filters are digital filters.
Generalized minimal residual method. In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this ...