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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. [ABSTRACT FROM AUTHOR]

Purpose: To present a fully automated treatment planning process for proton therapy including beam angle selection using a novel Bayesian optimization approach and previously developed constrained hierarchical fluence optimization method. Methods: We adapted our in‐house automated intensity modulated radiation therapy (IMRT) treatment planning system, which is based on constrained hierarchical optimization and referred to as ECHO (expedited constrained hierarchical optimization), for proton therapy. To couple this to beam angle selection, we propose using a novel Bayesian approach. By integrating ECHO with this Bayesian beam selection approach, we obtain a fully automated treatment planning framework including beam angle selection. Bayesian optimization is a global optimization technique which only needs to search a small fraction of the search space for slowly varying objective functions (i.e., smooth functions). Expedited constrained hierarchical optimization is run for some initial beam angle candidates and the resultant treatment plan for each beam configuration is rated using a clinically relevant treatment score function. Bayesian optimization iteratively predicts the treatment score for not‐yet‐evaluated candidates to find the best candidate to be optimized next with ECHO. We tested this technique on five head‐and‐neck (HN) patients with two coplanar beams. In addition, tests were performed with two noncoplanar and three coplanar beams for two patients. Results: For the two coplanar configurations, the Bayesian optimization found the optimal beam configuration after running ECHO for, at most, 4% of all potential configurations (23 iterations) for all patients (range: 2%–4%). Compared with the beam configurations chosen by the planner, the optimal configurations reduced the mandible maximum dose by 6.6 Gy and high dose to the unspecified normal tissues by 3.8 Gy, on average. For the two noncoplanar and three coplanar beam configurations, the algorithm converged after 45 iterations (examining <1% of all potential configurations). Conclusions: A fully automated and efficient treatment planning process for proton therapy, including beam angle optimization was developed. The algorithm automatically generates high‐quality plans with optimal beam angle configuration by combining Bayesian optimization and ECHO. As the Bayesian optimization is capable of handling complex nonconvex functions, the treatment score function which is used in the algorithm to evaluate the dose distribution corresponding to each beam configuration can contain any clinically relevant metric. [ABSTRACT FROM AUTHOR]

Purpose: We present a method for fully automated generation of high quality robust proton treatment plans using hierarchical optimization. To fill the gap between the two common extreme robust optimization approaches, that is, stochastic and worst‐case, a robust optimization approach based on the p‐norm function is used whereby a single parameter, p, can be used to control the level of robustness in an intuitive way. Methods: A fully automated approach to treatment planning using Expedited Constrained Hierarchical Optimization (ECHO) is implemented in our clinic for photon treatments. ECHO strictly enforces critical (inviolable) clinical criteria as hard constraints and improves the desirable clinical criteria sequentially, as much as is feasible. We extend our in‐house developed ECHO codes for proton therapy and integrate it with a new approach for robust optimization. Multiple scenarios accounting for both setup and range uncertainties are included (13scenarios), and the maximum/mean/dose‐volume constraints on organs‐at‐risk (OARs) and target are fulfilled in all scenarios. We combine the objective functions of the individual scenarios using the p‐norm function. The p‐norm with a parameter p=1 or p=∞ result in the stochastic or the worst‐case approach, respectively; an intermediate robustness level is obtained by employing p‐values in‐between. While the worst‐case approach only focuses on the worst‐case scenario(s), the p‐norm approach with a large p value (p≈20) resembles the worst‐case approach without completely neglecting other scenarios. The proposed approach is evaluated on three head‐and‐neck (HN) patients and one water phantom with different parameters, p∈1,2,5,10,20. The results are compared against the stochastic approach (p‐norm approach with p=1) and the worst‐case approach, as well as the nonrobust approach (optimized solely on the nominal scenario). Results: The proposed algorithm successfully generates automated robust proton plans on all cases. As opposed to the nonrobust plans, the robust plans have narrower dose volume histogram (DVH) bands across all 13 scenarios, and meet all hard constraints (i.e., maximum/mean/dose‐volume constraints) on OARs and the target for all scenarios. The spread in the objective function values is largest for the stochastic approach (p=1) and decreases with increasing p toward the worst‐case approach. Compared to the worst‐case approach, the p‐norm approach results in DVH bands for clinical target volume (CTV) which are closer to the prescription dose at a negligible cost in the DVH for the worst scenario, thereby improving the overall plan quality. On average, going from the worst‐case approach to the p‐norm approach with p=20, the median objective function value across all the scenarios is improved by 15% while the objective function value for the worst scenario is only degraded by 3%. Conclusion: An automated treatment planning approach for proton therapy is developed, including robustness, dose‐volume constraints, and the ability to control the robustness level using the p‐norm parameter p, to fit the priorities deemed most important. [ABSTRACT FROM AUTHOR]

Purpose: We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x‐ray spectrum that can accurately model the x‐ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Methods: Spectrum estimation is posed as an optimization problem with x‐ray spectrum as unknown variables, and a Kullback–Leibler (KL)‐divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated‐gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation–maximization (EM) method is also discussed. Results: In simulations, the proposed algorithm is seen to yield x‐ray spectra that closely match the ground truth and represent the attenuation process of x‐ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization‐based approach and EM. Conclusions: Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL‐divergence constraint can include a prior spectrum and appears to capture important features of x‐ray spectrum, allowing accurate and robust estimation of x‐ray spectrum in CT imaging. [ABSTRACT FROM AUTHOR]

Purpose: The streak artifacts caused by metal implants have long been recognized as a problem that limits various applications of CT imaging. In this work, the authors propose an iterative metal artifact reduction algorithm based on constrained optimization. Methods: After the shape and location of metal objects in the image domain is determined automatically by the binary metal identification algorithm and the segmentation of 'metal shadows' in projection domain is done, constrained optimization is used for image reconstruction. It minimizes a predefined function that reflects a priori knowledge of the image, subject to the constraint that the estimated projection data are within a specified tolerance of the available metal-shadow-excluded projection data, with image non-negativity enforced. The minimization problem is solved through the alternation of projection-onto-convex-sets and the steepest gradient descent of the objective function. The constrained optimization algorithm is evaluated with a penalized smoothness objective. Results: The study shows that the proposed method is capable of significantly reducing metal artifacts, suppressing noise, and improving soft-tissue visibility. It outperforms the FBP-type methods and ART and EM methods and yields artifacts-free images. Conclusions: Constrained optimization is an effective way to deal with CT reconstruction with embedded metal objects. Although the method is presented in the context of metal artifacts, it is applicable to general 'missing data' image reconstruction problems. [ABSTRACT FROM AUTHOR]