Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been actively investigated for regularizing image reconstruction problems by learning a prior for the object properties from training images. However, an analysis of the prior information learned by these deep networks and their ability to generalize to data that may lie outside the training distribution is still being explored. An inaccurate prior might lead to false structures being hallucinated in the reconstructed image and that is a cause for serious concern in medical imaging. In this work, we propose to illustrate the effect of the prior imposed by a reconstruction method by decomposing the image estimate into generalized measurement and null components. The concept of a hallucination map is introduced for the general purpose of understanding the effect of the prior in regularized reconstruction methods. Numerical studies are conducted corresponding to a stylized tomographic imaging modality. The behavior of different reconstruction methods under the proposed formalism is discussed with the help of the numerical studies.

翻译：地形图象的重建一般是一个错误的线性反向问题,这种错误的反向问题通常利用事先对寻求的物体财产的了解加以规范化。最近,深神经网络通过从培训图像中学习物体属性的事先知识,积极调查使图像重建问题正规化;然而,对这些深网络所学的先前信息及其对可能存在于培训分发之外的数据进行概括化的能力的分析仍在探讨之中。以前不准确的情况可能导致在重建的图像中出现假结构,并引起医疗成像的严重关切。在这项工作中,我们提议通过将图像估计分解为一般测量和无效组成部分来说明重建方法以前强加的图象重建方法的效果。引入幻觉图的概念是为了了解在常规化的重建方法中以前的效果的一般目的。进行数量学研究时,与一种结构化的成像模式相对应。拟议形式下的不同重建方法的行为在数字研究的帮助下得到了讨论。