Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing high-dimensional data because of the underexploration of the underlying structure. In this work, we propose to apply a tensor-based regression model to perform tomographic reconstruction. Furthermore, we explore the low-rank structure embedded in the corresponding tensor form. As a result, our proposed method efficiently reduces the dimensionality of the unknown parameters, which is particularly beneficial for ill-posed inverse problem suffering from insufficient data. We demonstrate the robustness of our proposed approach on synthetic noise-free data as well as on Gaussian noise-added data.

翻译：地形成像有助于揭示3D样本的内部结构。 古代重建方法将感兴趣的对象视为估计其价值的矢量。 但是,由于基础结构的探索不足,这种方法在分析高维数据方面可能效率低下。 在这项工作中,我们提议采用基于 10 的回归模型来进行地形重建。 此外,我们探索了嵌入相应色体的低级结构。结果,我们提出的方法有效地减少了未知参数的维度,这对数据不足造成的反向问题特别有利。我们显示了我们提议的关于合成无噪音数据以及高斯语噪音加增数据的方法的稳健性。