Fourier-Domain Analysis of the Iterative Landweber Algorithm

This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a 2-D tomography problem, which can be X-ray computed tomography (CT), positron emission tomography, and single photon emission CT. Two questions regarding to the linear iterative Landweber algorithm are considered. The first question is whether stopping early is equivalent to getting a minimum-norm solution. The second question is whether the low frequency components always converge first. Our answers to these two questions are No.