Image reconstruction in Multispectral Computed Tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. Existing methods necessitate computing the derivative of the forward map and potentially its regularized inverse. In this work, we present a simple yet highly effective algorithm for MSCT image reconstruction, utilizing iterative update mechanisms that leverage the full forward model in the forward step and a derivative-free adjoint problem. Our approach demonstrates both fast convergence and superior performance compared to existing algorithms, making it an interesting candidate for future work. We also discuss further generalizations of our method and its combination with additional regularization and other data discrepancy terms.

翻译：多谱计算机断层扫描（MSCT）中的图像重建需要求解一个具有挑战性的非线性逆问题，通常通过迭代优化算法来处理。现有方法需要计算前向映射的导数及其正则化逆。本文提出了一种简单而高效的MSCT图像重建算法，该算法利用迭代更新机制，在前向步骤中充分使用完整的前向模型，并采用无导数的伴随问题。与现有算法相比，我们的方法展现出更快的收敛速度和更优越的性能，使其成为未来研究的有力候选方案。我们还讨论了该方法进一步推广的可能性，以及其与额外正则化及其他数据差异项的结合。