A generalization of the EMML and ISRA algorithms for solving linear systems. (English) Zbl 1192.65042
Summary: From an algebraic point of view, the expectation-maximization maximum likelihood (EMML) algorithm and image space reconstruction algorithm (ISRA) algorithms for positron emission tomography can be considered as iterative procedures for solving a class of systems of linear equations. We introduce an algorithm \(A(p)\), \(p\in\mathbb R\), such that \(A(1)\) coincides with EMML and \(A(-1)\) with a version of ISRA. Some examples illustrate the speed of convergence. Applications are indicated to: (i) the Bernstein-Bézier representation; (ii) the B-spline interpolation; (iii) the inverse problem for Markov chains; (iv) the problem of finding the stationary distribution of a regular Markov chain.
MSC:
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
65C40 | Numerical analysis or methods applied to Markov chains |
65D07 | Numerical computation using splines |
65D05 | Numerical interpolation |
92C55 | Biomedical imaging and signal processing |
60J22 | Computational methods in Markov chains |