In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general linear operators and the corresponding filter-based regularization concept. We then introduce the TI-DFD for the Radon transform on $L^2(\R^2)$ and provide an exemplary construction using the TI wavelet transform. Presented numerical results clearly demonstrate the benefits of our approach over non-translation invariant counterparts.

翻译：本文通过平移不变对角框架分解（TI-DFD）解决计算机断层扫描中不适定重建问题的挑战。首先，我们回顾了一般线性算子的TI-DFD概念及相应的基于滤波的正则化方法。随后，我们针对$L^2(\R^2)$空间的Radon变换引入TI-DFD，并利用TI小波变换提供了一种典型构造。数值结果表明，该方法相较于非平移不变方法具有显著优势。