Abstract
Over recent years, deep learning methods have become an increasingly popular choice for solving tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point estimates for the reconstruction. However, especially in the analysis of ill-posed inverse problems, the study of uncertainties is essential. In our work, we apply generative flow-based models based on invertible neural networks to two challenging medical imaging tasks, i.e., low-dose computed tomography and accelerated medical resonance imaging. We test different architectures of invertible neural networks and provide extensive ablation studies. In most applications, a standard Gaussian is used as the base distribution for a flow-based model. Our results show that the choice of a radial distribution can improve the quality of reconstructions.
Highlights
The image reconstruction task arising in computed tomography (CT) or medical resonance imaging (MRI) can be formulated as an inverse problem
The focus here is on LoDoPaB-CT and fastMRI
In order to circumvent this problem, it is common to add a small amount of noise to the data to get a continuous distribution. This process is called dequantization and, in recent reviews, was done on all image datasets [69]. We found that this problem was not as severe for the medical imaging datasets studied in this paper; e.g., the LoDoPaB-CT dataset already used a dequantization of the discrete HU values
Summary
The image reconstruction task arising in computed tomography (CT) or medical resonance imaging (MRI) can be formulated as an inverse problem. Data-driven methods have been increasingly used in research and applications to solve inverse problems [1]. Instead of approximating a single point estimate, we are interested in the entire conditional distribution p(x|yδ) of the image given the noisy measurement data. Methods such as Markov chain Monte Carlo [9] or approximate Bayesian computation [10] have been used to estimate the unknown conditional distribution. These methods are often computationally expensive and unfeasible for large-scale imaging problems. One of the advantages is that flow-based models allow exact likelihood computation, allowing for maximum likelihood training
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