Some convergence results of OS-EM algorithm for ill-posed integral equations

ABSTRACT

In this paper, we study the properties of iteration OS-EM reconstruction method. We propose a speed-enhanced tomographic reconstruction algorithm that is accelerated to ordered-subset expectation-maximization by overrelaxation parameters. In the case of exact data, we concentrate on showing the monotonicity properties of the methods and convergence to the solution of the equation. Furthermore, in the case of perturbed data, we obtain some similar qualitative conclusions of the EM reconstruction method.

COMMUNICATED BY:

• Yongzhi Xu

KEYWORDS:

• Integral equation
• the OS-EM algorithm
• Kullback–Leibler distance
• regularization

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 30E25
• 65R32
• 65F22

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China [grant number 61271398] and K. C. Wong Magna Fund in Ningbo University.