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Tomographic Reconstruction and Regularisation with Search Space Expansion and Total Variation

Mohammad Majid al-Rifaie, Tim Blackwell

TL;DR

The paper tackles few-view tomographic reconstruction by reformulating TR as an optimisation problem and introducing two regularisation strategies: search space expansion (SSE) and total variation (TV). A minimalist Dispersive Flies Optimisation (DFO) swarm is used to search the high-dimensional space, with SSE gradually widening the feasible region and TV penalising image gradients to promote smooth, physiologically plausible reconstructions. Empirical results show that SSE and TV can reduce reproduction error ($e_2$) and yield reconstructions closer to ground truth than standard toolbox methods, with DFO-based methods achieving strong reproduction even when data are highly undersampled; comparisons with SHADE-ILS highlight trade-offs between data fidelity ($e_1$) and reproduction ($e_2$). The work suggests that hybrid or multiobjective extensions may further enhance fast, artefact-free reconstructions in the few-view regime, offering practical avenues for low-dose CT imaging.

Abstract

The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the long scanning time. This paper utilises the reformulation of the problem into an optimisation tasks, followed by using a swarm-based reconstruction from highly undersampled data where particles move in image space in an attempt to minimise the reconstruction error. The process is prone to noise and, in addition to the recently introduced search space expansion technique, a further smoothing process, total variation regularisation, is adapted and investigated. The proposed method is shown to produce lower reproduction errors compared to standard tomographic reconstruction toolbox algorithms as well as one of the leading high-dimensional optimisers on the clinically important Shepp-Logan phantom.

Tomographic Reconstruction and Regularisation with Search Space Expansion and Total Variation

TL;DR

The paper tackles few-view tomographic reconstruction by reformulating TR as an optimisation problem and introducing two regularisation strategies: search space expansion (SSE) and total variation (TV). A minimalist Dispersive Flies Optimisation (DFO) swarm is used to search the high-dimensional space, with SSE gradually widening the feasible region and TV penalising image gradients to promote smooth, physiologically plausible reconstructions. Empirical results show that SSE and TV can reduce reproduction error () and yield reconstructions closer to ground truth than standard toolbox methods, with DFO-based methods achieving strong reproduction even when data are highly undersampled; comparisons with SHADE-ILS highlight trade-offs between data fidelity () and reproduction (). The work suggests that hybrid or multiobjective extensions may further enhance fast, artefact-free reconstructions in the few-view regime, offering practical avenues for low-dose CT imaging.

Abstract

The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the long scanning time. This paper utilises the reformulation of the problem into an optimisation tasks, followed by using a swarm-based reconstruction from highly undersampled data where particles move in image space in an attempt to minimise the reconstruction error. The process is prone to noise and, in addition to the recently introduced search space expansion technique, a further smoothing process, total variation regularisation, is adapted and investigated. The proposed method is shown to produce lower reproduction errors compared to standard tomographic reconstruction toolbox algorithms as well as one of the leading high-dimensional optimisers on the clinically important Shepp-Logan phantom.
Paper Structure (13 sections, 7 equations, 3 figures, 8 tables)

This paper contains 13 sections, 7 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Tomography and reconstruction
  3. Regularisation
  4. Search space expansion
  5. Total Variation
  6. Minimalist swarm optimiser and TR
  7. Experiments and results
  8. Vanilla swarm and toolbox algorithms results
  9. Parameter tuning
  10. Search space expansion
  11. Total variation regularisation
  12. Comparison with SHADE-ILS algorithm
  13. Conclusion

Figures (3)

  • Figure 1: Phantoms
  • Figure 2: Visualsing the reconstruction process of Shepp-Logan phantom at different points in the optimisation process (every 10,000 FEs) and for varying number of expanding boxes, with phantom size of $32\times32$ and $6$ projections.
  • Figure 3: Reconstructing Shepp-Logan by the swarm optimiser without the smoothing methods (DFO-TR), the presented method with dual regularisation of search space expansion and the total variation (DFO-TR-$\mu$), the best standard TR toolbox algorithm (SIRT), and SHADE-ILS.