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.

Compensation of Missing Wedge Effects with Sequential Statistical Reconstruction in Electron Tomography

“…The minimum required number of sequences and iterations for each sequence depend on variance of sample and noise level. It is known that high number of iterations generates checkerboard artifacts in the images reconstructed with statistical methods if the images are not regularized during the iterations [31] . However, sMAP-EM can use large number of iterations and keep improving the images since the weight of regularization is never set to zero.…”

“…Therefore the resolution and the intensity contrast were enhanced. However, β was never set to 0 in order to avoid checkerboard artifacts observed when a high number of iterations is used without regularization [31] . The number of iterations in each sequence of sMAP-EM was chosen to be sufficiently large to satisfy convergence for reconstructions at different noise levels and different samples.…”

Image Inpainting Based on Inside–Outside Attention and Wavelet Decomposition

“…Each time, the image size was reduced by one-half, four dilated residual blocks [30] with a dilation factor of two were followed before decoding. To prevent the occurrence of checker-board artifacts [31], our decoder adopted the resize convolution [32] (bilinear interpolation was followed to resize the image) for upsampling. Reconstruction loss was used to optimize the rough network parameters explicitly.…”

A Bayesian approach for suppression of limited angular sampling artifacts in single particle 3D reconstruction

“…These three parameters together define the final regularization weight and the total number of iterations for the sMAP-EM, which strongly affect the quality of the resulting reconstruction. A small b value other than 0.0 is recommend for the final stage, since the absence of the regularization can yield a severe checkerboard artifacts with a large number of iterations when the measured projection data is noisy (You et al, 2007). The initial estimate of reconstruction is another user-defined input parameter, for which an image of uniform positive intensities is commonly used.…”