Assessing regularization in tomographic imaging via hallucinations in the null space

Sayantan Bhadra, Varun A. Kelkar, Frank J. Brooks, Mark A. Anastasio

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Tomographic imaging is an ill-posed linear inverse problem, and is often regularized using prior knowledge of the sought-after object property. However, typical hand-crafted priors such as sparsity-promoting penalties may be insufficient to comprehensively describe the prior knowledge of the object to-be-imaged. In order to utilize more detailed prior knowledge, data-driven methods using deep neural networks have recently been explored for learning a prior from existing image data. However, an analysis of the ability of such data-driven methods to generalize to data that may lie outside the training distribution is still under investigation. This is particularly critical for medical imaging applications. In order to address such concerns, in this work we propose to understand the effect of the prior imposed by a reconstruction method by comparing the null components of the sought-after object and its reconstructed estimate, when ground truth objects are available. The concept of a hallucination map is introduced for the purpose of assessing non-data-driven and data-driven regularization for image reconstruction. Numerical studies were conducted using stylized undersampled k-space measurements from publicly available magnetic resonance imaging (MRI) datasets. It is demonstrated that the proposed method can be employed to identify the source of false structures in estimates of the sought-after object for a given reconstruction method.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2021
Subtitle of host publicationImage Perception, Observer Performance, and Technology Assessment
EditorsFrank W. Samuelson, Sian Taylor-Phillips
ISBN (Electronic)9781510640276
StatePublished - 2021
EventMedical Imaging 2021: Image Perception, Observer Performance, and Technology Assessment - Virtual, Online
Duration: Feb 15 2021Feb 19 2021

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


ConferenceMedical Imaging 2021: Image Perception, Observer Performance, and Technology Assessment
CityVirtual, Online


  • deep learning
  • hallucinations
  • null space
  • regularization
  • tomographic imaging

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Biomaterials
  • Radiology Nuclear Medicine and imaging


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