Noise propagation in iterative reconstruction algorithms with line searches

In this paper we analyze the propagation of noise in iterative image reconstruction algorithms. We derive theoretical expressions for the general form of preconditioned gradient algorithms with line searches. The results are applicable to a wide range of iterative reconstruction problems, such as emission tomography, transmission tomography, and image restoration. A unique contribution of this paper comparing to our previous work [J. Qi (2003)] is that the line search is explicitly modeled and we do not use the approximation that the gradient of the objective function is zero. As a result, the error in the estimate of noise at early iterations is significantly reduced.