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. Therefore, in the absence of ground truth, quantifying the solution quality is highly desirable but under-explored. In this work, we address this challenge through Gaussian process modeling to flexibly and explicitly incorporate prior knowledge of sample features and experimental noises through the choices of the kernels and noise models. Our proposed method yields not only comparable reconstruction to existing practical reconstruction methods (e.g., regularized iterative solver for inverse problem) but also an efficient way of quantifying solution uncertainties. We demonstrate the capabilities of the proposed approach on various images and show its unique capability of uncertainty quantification in the presence of various noises.
翻译:层析成像虽然在广泛的应用中产生了革命性的影响,但由于有限和嘈杂的测量,它的逆问题是不适定的,因此不存在唯一解。因此,在缺乏地面真相的情况下,量化解决方案的质量是非常可取但很少被探索。在这项工作中,我们通过高斯过程建模来灵活和明确地将样品特征和实验噪声的先验知识纳入,通过核函数和噪声模型的选择。我们提出的方法不仅产生了可比的重建结果,而且还能够有效地量化解决方案的不确定性。我们展示了所提出方法在各种图像上的能力,并展示了它在不同噪声下量化解决方案不确定性的独特能力。