Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Traditional optimization-based reconstruction relies on regularization to address this issue; however, it faces its own challenge because the type of regularizer and choice of regularization parameter are a critical but difficult decision. Moreover, traditional reconstruction yields point estimates for the reconstruction with no further indication of the quality of the solution. In this work we address these challenges by exploring Gaussian processes (GPs). Our proposed GP approach yields not only the reconstructed object through the posterior mean but also a quantification of the solution uncertainties through the posterior covariance. Furthermore, we explore the flexibility of the GP framework to provide a robust model of the information across various length scales in the object, as well as the complex noise in the measurements. We illustrate the proposed approach on both synthetic and real tomography images and show its unique capability of uncertainty quantification in the presence of various types of noise, as well as reconstruction comparison with existing methods.

翻译：尽管对范围广泛的应用产生了革命性影响,但地形重建却由于其不理想的性质而受到影响,因为由于测量有限和噪音,没有独特的解决办法。传统的优化型重建依靠正规化来解决这一问题;然而,由于正规化和选择正规化参数的种类是一个关键但困难的决定,它面临着自己的挑战。此外,传统的重建可产生重建的点估计数,而没有进一步说明解决方案的质量。在这项工作中,我们探索高山进程(GPs)来应对这些挑战。我们提议的GP方法不仅通过后方语言产生重建对象,而且还通过后方变量量化解决方案的不确定性。此外,我们探索GP框架的灵活性,以提供一个强有力的模型,提供该目标中跨不同长度的信息,以及测量中的复杂噪音。我们介绍了关于合成图像和真实图像的拟议方法,并展示了在存在各种噪音时对不确定性进行量化的独特能力,以及与现有方法进行重建比较。