Spectral CT image reconstruction using a constrained optimization approach—An algorithm for AAPM 2022 spectral CT grand challenge and beyond

• Published in: Medical physics (Lancaster) Vol. 51; no. 5; pp. 3376 - 3390
• Main Authors: Hu, Xiaoyu, Jia, Xun
• Format: Journal Article
• Language: English
• Published: United States 01.05.2024
• Subjects: Algorithms; deep learning; Humans; Image Processing, Computer-Assisted - methods; Phantoms, Imaging; reconstruction; spectral CT; Tomography, X-Ray Computed - methods; spectral CT; deep learning; reconstruction
• ISSN: 0094-2405; 2473-4209; 1522-8541; 2473-4209
• DOI: 10.1002/mp.16877

Background CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions PROSPECT algorithm achieved a high degree of accuracy and computational efficiency.