A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction

TL;DR

This paper introduces a novel tensor-based dictionary learning method for tomographic image reconstruction, leveraging third-order tensor representations and sparse coding to improve reconstruction quality.

Contribution

It presents a new tensor formulation for dictionary learning and reconstruction, differing from prior methods by using third-order tensors and a convex optimization approach.

Findings

Tensor formulation yields highly sparse representations.

Improved reconstruction quality with compact feature representation.

Effective in capturing repeated image features.

Abstract

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.