A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction
This work addresses tomographic reconstruction for medical or scientific imaging, but it is incremental as it builds on existing dictionary learning methods with a tensor formulation.
The authors tackled tomographic image reconstruction by proposing a tensor-based dictionary learning approach, which achieved very sparse representations of both training images and reconstructions due to compact feature representation.
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that a) we use a third-order tensor representation for our images and b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.