CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction
H. Gupta, K.H. Jin, H.Q. Nguyen, M.T. McCann, M. Unser
IEEE Transactions on Medical Imaging, in press.
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We present a new image reconstruction method that replaces the projector in a projected gradient descent (PGD) with a convolutional neural network (CNN). Recently, CNNs trained as image-to-image regressors have successfully been used to solve inverse problems in imaging. However, unlike existing iterative image reconstruction algorithms, these CNN-based approaches usually lack a feedback mechanism to enforce that the reconstructed image is consistent with the measurements. We propose a relaxed version of PGD wherein gradient descent enforces measurement consistency, while a CNN recursively projects the solution closer to the space of desired reconstruction images. We show that this algorithm is guaranteed to converge and, under certain conditions, converges to a local minimum of a non-convex inverse problem. Finally, we propose a simple scheme to train the CNN to act like a projector. Our experiments on sparse-view computed-tomography reconstruction show an improvement over total variation-based regularization, dictionary learning, and a state-of-the-art deep learning-based direct reconstruction technique.