3. A Fast Algebraic Image Reconstruction Method for a Clinical PET Scanner
Taiga Yamaya, Takashi Obi*, Masahiro Yamaguchi*, Nagaaki Ohyama* and Hideo Murayama (*Imaging Sci. & Eng. Lab., Tokyo Inst. of Tech.)
Keywords: image reconstruction, positron emission tomography (PET), nuclear medicine
Algebraic reconstruction methods, such as natural pixel decomposition (NPD), have been successfully used to improve quality of positron emission tomography (PET) images by accurate modeling of the measurement system, while the conventional filtered backprojection (FBP) method is based on an inaccurate system model. These algebraic methods, however, require extensive computation since they deal with a large matrix of the same dimension as that of the measurement data.
We proposed a fast image reconstruction method based on an algebraic technique using approximation and pre-processing. The proposed method estimates each element of the sampled image using a subset of measurement data, while conventional algebraic reconstruction methods use all the data. For each image point to be reconstructed, the subset contains the measurement data that contribute significantly to the image point. Consequently the dimension of the matrix becomes small, and operators to obtain the PET image directly from subsets of measurement data are pre-computed and stored for each image point. In addition, the constraint that ensures quantitative reconstruction, which NPD does not deal with, is easily installed in the proposed method because of the element-by-element implementation. Since image reconstruction in PET is usually an ill-conditioned inverse problem, the constraint effectively improves image quality. At this stage, we suppose that scatter coincidences, random coincidences and attenuation are corrected completely.
After optimizing the size of the subset using numerical simulation, we applied the proposed method to experimental data for the ECAT EXACT HR+ (Siemens/CTI) scanner operating in 2D mode. The phantom, placed at the center of the scanner, consisted of a cylindrical vessel (200 mm in diameter and 190 mm in length) with 1.42 mCi 18F activity water and two rods with water and air respectively. After the normalization and attenuation correction, the reconstructed images were obtained using the proposed method, NPD and FBP. Here the scatter correction was not implemented. Two FOMs, cold contrast recovery (cCR) and the normalized standard deviation (NSD), were used to evaluate the image quality. The trade-off between the NSD and the cCR is shown in Fig. 3, using the proposed method and NPD with different values of regularization parameters and FBP with a ramp filter of different cut-off frequencies. In order to evaluate the effect of the constraint, the proposed method with no constraint was also applied. We clearly see that the proposed method has a higher cCR value for any particular value of background noise level. The result also shows that the constraint corrects the contrast recovery loss caused by the selection of the measurement data. The averaged calculation time on an Alpha 500MHz PC to reconstruct one image slice using the proposed method is 4.7 sec., while NPD requires 28 min. and FBP requires 2.8 sec. The proposed method has an advantage in calculation time over NPD and has a similar time to FBP.
In summary, our proposed method produces images with almost the same or superior quality to the conventional algebraic methods and has a similar computation time to FBP.
Yamaya, T., Obi, T., Yamaguchi, M., Kita, K., Ohyama, N. and Murayama, H.: IEEE Trans. Nucl. Sci., 47, 1670-1675, 2000.
[Back to index]