Towards an Algebraic Multigrid Method for Tomographic Image Reconstruction – Improving Convergence of Art
نویسندگان
چکیده
In this paper we introduce a multigrid method for sparse, possibly rankdeficient and inconsistent least squares problems arising in the context of tomographic image reconstruction. The key idea is to construct a suitable AMG method using the Kaczmarz algorithm as smoother. We first present some theoretical results about the correction step and then show by our numerical experiments that we are able to reduce the computational time to achieve the same accuracy by using the multigrid method instead of the standard Kaczmarz algorithm.
منابع مشابه
A full multigrid technique to accelerate an ART scheme for tomographic image reconstruction
Tomographic reconstruction is the process of reconstructing a 3-D object or its cross section from several of its 2-D projection images. The object is illuminated by a cone-beam of Xrays, where the signal is attenuated by the object. Due to its speed filtered back projection (FBP) still is state-of-the-art in 3-D reconstruction for clinical use where time matters. But considering the accuracy a...
متن کاملTowards a Variational Approach to Regularized Tomographic Reconstruction
The classical Kaczmarz’s method, which is the basis for many Algebraic Reconstruction Techniques (ART), is very popular in the field of image reconstruction. However, this algorithm gives only satisfactory results for consistent data. For inconsistent data, which is the case in practice, the algorithm has some problems with respect to convergence. In this master’s thesis, we formulated the reco...
متن کاملConvergence of ART in Few Projections
Algebraic Reconstruction Technique (ART) is an iterative algorithm to obtain reconstruction from projections in a finite number of iterations. The present paper discuses the convergence achieved in small number of iteration even when projection data is available in only four directions. Keywords-ART, Image Reconstruction, Convergence, Projections, Computed Tomography
متن کاملMulticore Performance of Block Algebraic Iterative Reconstruction Methods
Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the Algebraic Reconstruction Techniques (ART) and the Simultaneous Iterative Reconstruction Techniques (SIRT), both of which rely on semi-convergence. Block versions of these methods, based on a partitioning of the linear system, are able t...
متن کاملAlgebraic Full Multigrid in Image Reconstruction
In this paper we propose an algebraic full multigrid algorithm for efficient and robust numerical solution of arbitrary linear systems of equations arising in image reconstruction from projections in computerized tomography. Numerical experiments and comparisons with the classical Kaczmarz algebraic reconstruction technique are presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006