  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.
