Understanding edge artifacts of the OSEM algorithm in emission tomography

Angelina V. Nesterova; Natalya V. Denisova; Pavel S. Ruzankin

doi:10.1515/jiip-2024-0070

Article

Understanding edge artifacts of the OSEM algorithm in emission tomography

Angelina V. Nesterova , Natalya V. Denisova and Pavel S. Ruzankin

Published/Copyright: June 25, 2025

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From the journal Journal of Inverse and Ill-posed Problems Volume 33 Issue 4

Abstract

A significant challenge in achieving accurate results with the OSEM algorithm in emission tomography is the emergence of edge artifacts at high-contrast boundaries. However, the underlying cause of these artifacts is not well understood. This study aims to investigate the mechanism behind their formation. Image reconstruction was modeled using the MLEM algorithm for the one-dimensional case and the OSEM algorithm for the 3D case closely reflecting clinical practice. This was complemented by an analysis of the underlying formulas of these algorithms. The primary mechanism behind the emergence of edge artifacts is not their occurrence at a specific iteration, but the OSEM algorithm’s tendency to preserve these artifacts, along with other short-wavelength disturbances, over numerous iterations. Thus, filtering of the reconstructed images is necessary, at least during intermediate iterations, to eliminate edge artifacts. Furthermore, it has been observed that these artifacts arise from the inherent nature of the OSEM algorithm, rather than from insufficient information in the observed data.

Keywords: SPECT; MLEM; OSEM; edge artifacts; PSF reconstruction

MSC 2020: 65R32; 78A46; 65C99

Funding source: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences

Award Identifier / Grant number: FWNF-2024-0002

Funding statement: The work was performed according to the Government research assignment for Sobolev Institute of Mathematics SB RAS, project FWNF-2024-0002.

A Appendix

For the one-dimensional example with FWHM = 4 and the initial solution in the form of a wave with wavelength of four voxels:

f 4 ⁢ j 0 = f 4 ⁢ j + 1 0 = 1 , f 4 ⁢ j + 2 0 = f 4 ⁢ j + 3 0 = 10 ,

the following results were obtained (Figure 12).

$Figure 12 One-dimensional model reconstructed by the MLEM algorithm over 100 to 10 million iterations, where the initial solution f ( 0 ) {f^{(0)}} is a wave with wavelength of four voxels. The red line represents the numerical solution, the green line is the vector g, the light blue line is the initial approximation, and the blue line is the original model.$

Figure 12

One-dimensional model reconstructed by the MLEM algorithm over 100 to 10 million iterations, where the initial solution f ( 0 ) is a wave with wavelength of four voxels. The red line represents the numerical solution, the green line is the vector g, the light blue line is the initial approximation, and the blue line is the original model.

For the three-dimensional example, using the initial solution in the form of wave with wavelength of four voxels yields the following results (Figure 13 corresponds to the numerical experiment without Poisson “noise”, Figure 14 corresponds to simulation with Poisson “noise”).

$Figure 13 3D simulation without Poisson “noise”. The top row shows cross-sections passing through the center of the middle spheres in the model reconstructed by the OSEM algorithm for n iterations. The bottom row shows profiles passing through the center of the middle spheres of the model for n iterations. The blue line corresponds to the exact model, and the red line corresponds to the model reconstructed by the OSEM algorithm. The first column shows the initial solution f ( 0 ) {f^{(0)}} . The top row corresponds to a constant initial solution, while the bottom row corresponds to an initial solution in the form of a wave with wavelength of four voxels.$

Figure 13

3D simulation without Poisson “noise”. The top row shows cross-sections passing through the center of the middle spheres in the model reconstructed by the OSEM algorithm for n iterations. The bottom row shows profiles passing through the center of the middle spheres of the model for n iterations. The blue line corresponds to the exact model, and the red line corresponds to the model reconstructed by the OSEM algorithm. The first column shows the initial solution f ( 0 ) . The top row corresponds to a constant initial solution, while the bottom row corresponds to an initial solution in the form of a wave with wavelength of four voxels.

$Figure 14 3D simulation with Poisson “noise”. The top row shows cross-sections passing through the center of the middle spheres in the model reconstructed by the OSEM algorithm for n iterations. The bottom row shows profiles passing through the center of the middle spheres of the model for n iterations. The blue line corresponds to the exact model, and the red line corresponds to the model reconstructed by the OSEM algorithm. The first column shows the initial solution f ( 0 ) {f^{(0)}} . The top row corresponds to a constant initial solution, while the bottom row corresponds to an initial solution in the form of a wave with wavelength of four voxels.$

Figure 14

3D simulation with Poisson “noise”. The top row shows cross-sections passing through the center of the middle spheres in the model reconstructed by the OSEM algorithm for n iterations. The bottom row shows profiles passing through the center of the middle spheres of the model for n iterations. The blue line corresponds to the exact model, and the red line corresponds to the model reconstructed by the OSEM algorithm. The first column shows the initial solution f ( 0 ) . The top row corresponds to a constant initial solution, while the bottom row corresponds to an initial solution in the form of a wave with wavelength of four voxels.

The next numerical experiments are one-dimensional and consider different values of FWHM.

Figure 15

One-dimensional model reconstructed by the MLEM algorithm for different values of the FWHM parameter and the number of iterations n. A constant straight line is used as the initial solution. The red line represents the numerical solution, the green line is the vector g, the light blue line is the initial approximation, and the blue line is the original model.

Figure 16

The blue line corresponds to the original model, the red line is the numerical solution obtained at the 100th iteration, and the yellow line is the solution obtained by the standard method for solving the system of linear equations via PLU decomposition.

Figures 15 and 16 show, for different values of FWHM, the behavior of the MLEM algorithm and of the standard solver for systems of linear equations. Notably, the standard solver struggles with large FWHM values, likely due to insufficient precision in the computer representation of real numbers (64-bit real numbers were used), whereas MLEM provides “relatively satisfactory” solutions in these cases.

References

[1] B. Bai and P. D. Esser, The effect of edge artifacts on quantification of positron emission tomography, IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), IEEE Press, Piscataway (2010), 2263–2266. 10.1109/NSSMIC.2010.5874186Search in Google Scholar

[2] N. V. Denisova, Mathematical simulation modeling in nuclear medicine for optimizing diagnostic accuracy of SPECT/CT method, J. Med. Phys. (2023), no. 3, 45–62. 10.52775/1810-200X-2023-99-3-45-62Search in Google Scholar

[3] N. V. Denisova, M. A. Gurko, I. P. Kolinko, A. A. Ansheles and V. B. Sergienko, Virtual platform for simulation computer modeling of radionuclide imaging in nuclear cardiology: Comparison with clinical data, Digit. Diagn. 4 (2023), no. 4, 492–508. 10.17816/DD595696Search in Google Scholar

[4] T. Kangasmaa, A. Sohlberg and J. T. Kuikka, Reduction of collimator correction artefacts with bayesian reconstruction in spect, Int. J. Mol. Imaging 2011 (2011), Article ID 630813. 10.1155/2011/630813Search in Google Scholar PubMed PubMed Central

[5] D. Kidera, K. Kihara, G. Akamatsu, S. Mikasa, T. Taniguchi and Y. Tsutsui, The edge artifact in the point-spread function-based PET reconstruction at different sphere-to-background ratios of radioactivity, Ann. Nucl. Med. 30 (2016), no. 2, 97–103. 10.1007/s12149-015-1036-9Search in Google Scholar PubMed

[6] K. Lange and R. Carson, EM reconstruction algorithms for emission and transmission tomography, J. Comp. Assisted Tomography 8 (1984), no. 2, 306–316. Search in Google Scholar

[7] A. V. Nesterova and N. V. Denisova, Pitfalls on the way to quantify the severity of oncological lesions in diagnostic nuclear medicine, J. Tech. Phys. 92 (2022), no. 7, 1018–1027. 10.21883/TP.2022.07.54482.331-21Search in Google Scholar

[8] J. Nuyts, Unconstrained image reconstruction with resolution modelling does not have a unique solution, EJNMMI Phys. 1 (2014), Paper No. 98. 10.1186/s40658-014-0098-4Search in Google Scholar PubMed PubMed Central

[9] D. G. Politte and D. L. Snyder, The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography, IEEE Trans. Nuclear Sci. 35 (1988), no. 1, 608–610. 10.1109/23.12796Search in Google Scholar

[10] L. A. Shepp and Y. Vardi, Maximum likelihood reconstruction for emission tomography, IEEE Trans. Med. Imaging 1 (1983), 113–122. 10.1109/TMI.1982.4307558Search in Google Scholar PubMed

[11] H. Shinohara and T. Hashimoto, Mechanism of edge artifacts in PSF reconstruction, Med. Imag. Tech. 40 (2022), no. 5, 261–272. Search in Google Scholar

[12] H. Shinohara, K. Hori and T. Hashimoto, Deep learning study on the mechanism of edge artifacts in point spread function reconstruction for numerical brain images, Ann. Nucl. Med. 37 (2023), no. 11, 596–604. 10.1007/s12149-023-01862-9Search in Google Scholar PubMed

[13] D. L. Snyder, M. I. Miller, L. J. Thomas and D. G. Politte, Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography, IEEE Trans. Med. Imaging 6 (1987), no. 3, 228–238. 10.1109/TMI.1987.4307831Search in Google Scholar PubMed

[14] S. Tong, A. M. Alessio, K. Thielemans, C. Stearns, S. Ross and P. E. Kinahan, Properties of edge artifacts in PSF-based PET reconstruction, IEEE Nuclear Science Symposuim & Medical Imaging Conference, IEEE Press, Piscataway (2010), 3649–3652. 10.1109/NSSMIC.2010.5874493Search in Google Scholar

[15] S. Tong, A. M. Alessio, K. Thielemans, C. Stearns, S. Ross and P. E. Kinahan, Properties and mitigation of edge artifacts in psf-based pet reconstruction, IEEE Trans. Nuclear Sci. 58 (2011), no. 5, 2264–2275. 10.1109/TNS.2011.2164579Search in Google Scholar

[16] Y. Tsutsui, S. Awamoto, K. Himuro, Y. Umezu, S. Baba and M. Sasaki, Edge artifacts in point spread function-based pet reconstruction in relation to object size and reconstruction parameters, Asia Ocean J. Nucl. Med. Biol. 5 (2017), no. 2, 134–143. Search in Google Scholar

[17] S. Yamaguchi, K. Wagatsuma, K. Miwa, K. Ishii, K. Inoue and M. Fukushi, Bayesian penalized-likelihood reconstruction algorithm suppresses edge artifacts in PET reconstruction based on point-spread-function, Phys. Med. 47 (2018), 73–79. 10.1016/j.ejmp.2018.02.013Search in Google Scholar PubMed

Received: 2024-10-20

Accepted: 2025-03-23

Published Online: 2025-06-25

Published in Print: 2025-08-01

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Articles in the same Issue

https://doi.org/10.1515/jiip-2024-0070

Keywords for this article

SPECT; MLEM; OSEM; edge artifacts; PSF reconstruction