Convolutional analysis operator learning: Application to sparse-view CT : (Invited Paper)

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Convolutional analysis operator learning (CAOL) methods train an autoencoding convolutional neural network (CNN) in an unsupervised learning manner, to more accurately solve inverse problems. Block Proximal Gradient method using a Majorizer (BPG-M) achieved fast and convergent CAOL, by using sharp majorizers and the momentum terms. This paper proposes a model-based image reconstruction (MBIR) method using autoencoding CNNs trained via CAOL, for sparse-view computational tomography (CT). We apply BPG-M to rapidly and stably solve the corresponding block multi-nonconvex optimization problem. Numerical experiments show that, for sparse-view CT, 1) the proposed MBIR method outperforms the standard MBIR method using edge-preserving regularization; 2) larger parameter dimensions of autoencoding CNNs improve reconstruction accuracy of the proposed MBIR method; and 3) when using BPG-M, sharper majorization is more critical for accelerating its convergence than giving more weights on extrapolation.