Tomographic Image Reconstruction using Training images

TL;DR

This paper introduces a novel tomographic image reconstruction algorithm that leverages training images to create a nonnegative dictionary, enabling sparse representation and improved reconstruction quality, especially in low-dose, few-projection scenarios.

Contribution

The paper presents a new dictionary-based regularization method for tomographic reconstruction using training images, with reduced computational complexity and competitive performance.

Findings

Performs well in low-dose, few-projection settings

Includes more texture and correct edges than total variation regularization

Uses nonnegative matrix factorization for dictionary construction

Abstract

We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the training images; this problem is formulated as a regularized non-negative matrix factorization. Incorporating the dictionary as a prior in a convex reconstruction problem, we then find an approximate solution with a sparse representation in the dictionary. The dictionary is applied to non-overlapping patches of the image, which reduces the computational complexity compared to other algorithms. Computational experiments clarify the choice and interplay of the model parameters and the regularization parameters, and we show that in few-projection low-dose settings our algorithm is competitive with total variation regularization and tends to include more texture and more correct edges.