# A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction

arXiv: https://arxiv.org/abs/1506.04954 · HTML: https://mlsanity.com/paper/1506.04954/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2015.

## Built on by (most cited first, 6 of 6)

- [High-Order Multilinear Discriminant Analysis via Order-textitn Tensor Eigendecomposition](https://mlsanity.com/paper/2205.09191/) (2022)
- [T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network based on Tensor T-product Operator](https://mlsanity.com/paper/2306.04240/) (2023)
- [Coseparable Nonnegative Tensor Factorization With T-CUR Decomposition](https://mlsanity.com/paper/2401.16836/) (2024)
- [Tensor-Tensor Products, Group Representations, and Semidefinite Programming](https://mlsanity.com/paper/2507.12729/) (2025)
- [Online multidimensional dictionary learning](https://mlsanity.com/paper/2503.09337/) (2025)
- [Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems](https://mlsanity.com/paper/2503.18190/) (2025)

## Abstract (arXiv)

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.