A tensor-based dictionary learning approach to tomographic image reconstruction

Sara Soltani, Misha E. Kilmer, Per Christian Hansen

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalBIT Numerical Mathematics
Issue number4
Pages (from-to)1425–1454
Number of pages30
Publication statusPublished - 2016


  • Tensor decomposition
  • Tensor dictionary learning
  • Inverse problem
  • Regularization
  • Sparse representation
  • Tomographic image reconstruction

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