AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

作者：Hansen Per Christian^*; Saxild Hansen Maria

来源：Journal of Computational and Applied Mathematics, 2012, 236(8): 2167-2178.

DOI：10.1016/j.cam.2011.09.039

• ART methods
• SIRT methods
• Semi-convergence
• Relaxation parameters
• Stopping rules
• Tomographic imaging

We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are implemented: Algebraic Reconstruction Techniques (ART) and Simultaneous Iterative Reconstruction Techniques (SIRT). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter and the stopping rule. The relaxation parameter can be fixed, or chosen adaptively in each iteration: in the former case we provide a new %26quot;training%26quot; algorithm that finds the optimal parameter for a given test problem. The stopping rules provided are the discrepancy principle, the monotone error rule, and the NCP criterion: for the first two methods %26quot;training%26quot; can be used to find the optimal discrepancy parameter.

• 出版日期2012-2