title: Range Condition and ML-EM Checkerboard Artifacts.
abstract: The expectation maximization (EM) algorithm for the maximum likelihood (ML) image reconstruction criterion generates severe checkerboard artifacts in the presence of noise. A classical remedy is to impose an a priori constraint for a penalized ML or maximum a posteriori probability solution. The penalty reduces the checkerboard artifacts and also introduces uncertainty because a priori information is usually unknown in clinic. Recent theoretical investigation reveals that the noise can be divided into two components: one is called null-space noise and the other is range-space noise. The null-space noise can be numerically estimated using filtered backprojection (FBP) algorithm. By the FBP algorithm, the null-space noise annihilates in the reconstruction while the range-space noise propagates into the reconstructed image. The aim of this work is to investigate the relation between the null-space noise and the checkerboard artifacts in the ML-EM reconstruction from noisy projection data. Our study suggests that removing the null-space noise from the projection data could improve the signal-to-noise ratio of the projection data and, therefore, reduce the checkerboard artifacts in the ML-EM reconstructed images. This study reveals an in-depth understanding of the different noise propagations in analytical and iterative image reconstructions, which may be useful to single photon emission computed tomography, where the noise has been a major factor for image degradation. The reduction of the ML-EM checkerboard artifacts by removing the null-space noise avoids the uncertainty of using a priori penalty.
authors.affiliation: Cubic Imaging LLC, 264 Grove St., Auburndale, MA 02466, USA and the Department of Radiology, State University of New York, Stony Brook, NY 11794, USA (e-mail:  jyou@cubic-imaging.com ).
authors.forename: Jiangsheng
authors.initials: J
authors.lastname: You
authors.forename: Jing
authors.initials: J
authors.lastname: Wang
authors.forename: Zhengrong
authors.initials: Z
authors.lastname: Liang