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.

. Purpose: Deep learning-based image super-resolution (DL-SR) has shown great promise in medical imaging applications. To date, most of the proposed methods for DL-SR have only been assessed using traditional measures of image quality (IQ) that are commonly employed in the field of computer vision. However, the impact of these methods on objective measures of IQ that are relevant to medical imaging tasks remains largely unexplored. We investigate the impact of DL-SR methods on binary signal detection performance. Approach: Two popular DL-SR methods, the super-resolution convolutional neural network and the super-resolution generative adversarial network, were trained using simulated medical image data. Binary signal-known-exactly with background-known-statistically and signal-known-statistically with background-known-statistically detection tasks were formulated. Numerical observers (NOs), which included a neural network-approximated ideal observer and common linear NOs, were employed to assess the impact of DL-SR on task performance. The impact of the complexity of the DL-SR network architectures on task performance was quantified. In addition, the utility of DL-SR for improving the task performance of suboptimal observers was investigated. Results: Our numerical experiments confirmed that, as expected, DL-SR improved traditional measures of IQ. However, for many of the study designs considered, the DL-SR methods provided little or no improvement in task performance and even degraded it. It was observed that DL-SR improved the task performance of suboptimal observers under certain conditions. Conclusions: Our study highlights the urgent need for the objective assessment of DL-SR methods and suggests avenues for improving their efficacy in medical imaging applications.

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In recent years, generative adversarial networks (GANs) have gained tremendous popularity for potential applications in medical imaging, such as medical image synthesis, restoration, reconstruction, translation, as well as objective image quality assessment. Despite the impressive progress in generating high-resolution, perceptually realistic images, it is not clear if modern GANs reliably learn the statistics that are meaningful to a downstream medical imaging application. In this work, the ability of a state-of-the-art GAN to learn the statistics of canonical stochastic image models (SIMs) that are relevant to objective assessment of image quality is investigated. It is shown that although the employed GAN successfully learned several basic first-and second-order statistics of the specific medical SIMs under consideration and generated images with high perceptual quality, it failed to correctly learn several per-image statistics pertinent to the these SIMs, highlighting the urgent need to assess medical image GANs in terms of objective measures of image quality.