Sparse aNETT for Solving Inverse Problems with Deep Learning
This work addresses inverse problems in medical imaging, such as CT reconstruction, with incremental improvements in robustness and generalization.
The authors tackled the problem of solving inverse problems in imaging by proposing a sparse reconstruction framework (aNETT) that uses a trained autoencoder as a nonlinear sparsifying transform, with results demonstrating improved generalization and stability over existing methods in sparse view CT.
We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an autoencoder network $D \circ E$ with $E$ acting as a nonlinear sparsifying transform and minimize a Tikhonov functional with learned regularizer formed by the $\ell^q$-norm of the encoder coefficients and a penalty for the distance to the data manifold. We propose a strategy for training an autoencoder based on a sample set of the underlying image class such that the autoencoder is independent of the forward operator and is subsequently adapted to the specific forward model. Numerical results are presented for sparse view CT, which clearly demonstrate the feasibility, robustness and the improved generalization capability and stability of aNETT over post-processing networks.