Do CNNs solve the CT inverse problem?

Objective: This work examines the claim made in the literature that the inverse problem associated with image reconstruction in sparse-view computed tomography (CT) can be solved with a convolutional neural network (CNN). Methods: Training and testing image/data pairs are generated in a dedicated breast CT simulation for sparse-view sampling, using two different object models. The trained CNN is tested to see if images can be accurately recovered from their corresponding sparse-view data. For reference, the same sparse-view CT data is reconstructed by the use of constrained total-variation (TV) minimization (TVmin), which exploits sparsity in the gradient magnitude image (GMI). Results: Using sparse-view data from images either in the training or testing set, there is a significant discrepancy between the image obtained with the CNN and the image that generated the data. For the same simulated scanning conditions, TVmin is able to accurately reconstruct the test image. Conclusion: We find that the sparse-view CT inverse problem cannot be solved for the particular published CNN-based methodology that we chose and the particular object model that we tested. Furthermore, this negative result is obtained for conditions where TVmin is able to recover the test images. Significance: The inability of the CNN to solve the inverse problem associated with sparse-view CT, for the specific conditions of the presented simulation, draws into question similar unsupported claims being made for the use of CNNs to solve inverse problems in medical imaging.