A tailored ML-EM algorithm for reconstruction of truncated projection data using few view angles

Abstract

Dedicated cardiac single photon emission computed tomography (SPECT) systems have the advantage of high speed and sensitivity at no loss, or even a gain, in resolution. The potential drawbacks of these dedicated systems are data truncation by the small field of view (FOV) and the lack of view angles. Serious artifacts, including streaks outside the FOV and distortion in the FOV, are introduced to the reconstruction when using the traditional emission data maximum-likelihood expectation-maximization (ML-EM) algorithm to reconstruct images from the truncated data with a small number of views. In this note, we propose a tailored ML-EM algorithm to suppress the artifacts caused by data truncation and insufficient angular sampling by reducing the image updating step sizes for the pixels outside the FOV. As a consequence, the convergence speed for the pixels outside the FOV is decelerated. We applied the proposed algorithm to truncated analytical data, Monte Carlo simulation data and real emission data with different numbers of views. The computer simulation results show that the tailored ML-EM algorithm outperforms the conventional ML-EM algorithm in terms of streak artifacts and distortion suppression for reconstruction from truncated projection data with a small number of views.

Figure 1

The change of $\sum _i{a}_{ij}$ before and after array expansion. The pixel x_j outside the FOV is affected by the array expansion.

Figure 2

From left to right: the 110^th, 120^th and 128^th axial slices of the 3D heart phantom. The FOV covered by the small detector is indicated by the dashed circle.

Figure 3

(a) The Jaszczak torso phantom. (b) The Siemens E-CAM Signature Series^® SPECT scanner used in the experiment.

Figure 4

Images of the analytical heart phantom reconstructed by the conventional ML-EM and the tailored ML-EM algorithms using different number of views. The projections were truncated and 500 iterations were applied.

Figure 5

The vertical profiles through the center of slice 128 of the analytical heart phantom and the reconstructed images using the conventional ML-EM and the tailored ML-EM algorithms. The images were reconstructed from 60, 20, and 10 truncated projections. The solid line represents the true heart phantom, the solid line with plus sign represents the tailored ML-EM reconstruction and the dash line represents the conventional ML-EM reconstruction.

Figure 6

MSE as a function of relative contrast in the reconstructed analytical heart phantom using conventional ML-EM and tailored ML-EM algorithms. The points on the curves represent the numbers of views. For each curve, the view number increases from the left side to the right side.

Figure 7

Sample reconstructed central axial slices of the conventional and tailored ML-EM reconstructions at different iterations in the analytical heart phantom experiment. All images were reconstructed from 20 truncated projections.

Figure 8

The reconstruction results of Monte Carlo simulation using the NCAT phantom. The first column shows the central slices of the reconstructions. Vertical long-axis (VLA), short-axis (SA), and horizontal long-axis (HLA) cuts are shown in the last three columns. 10 iterations were used.

Figure 9

The vertical profile curves for slice 128 of reconstructed images with 60 (top row) and 14 views (bottom row). Solid lines on slice 128 of the NCAT phantom indicate the profile positions. The profiles on the right side correspond to the lines from left to right in the left-hand image.

Figure 10

The vertical profiles for slice 128 of the reconstructed images using conventional ML-EM and tailored ML-EM algorithms. The images were reconstructed from 60, 20, and 10 truncated projections. Solid lines on slice 128 of the reconstructed images indicate the profile positions.

Figure 11

The reconstruction results obtained from physical phantom study. From top to bottom: the reconstruction results of 60, 20 and 10 truncated projections, respectively. The first column shows the central slices of the reconstructions. Vertical long-axis (VLA), short-axis (SA), and horizontal long-axis (HLA) cuts are shown in the last three columns. 30 iterations were used.