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Dynamic computerized tomography using inexact models and motion estimation

Gesa Sarnighausen, Anne Wald, Alexander Meaney

TL;DR

The iterative RESESOP-Kaczmarz method can - under certain conditions and by exploiting the modeling error - reconstruct dynamic objects at different time points even if the exact motion is unknown, however, the method is very time-consuming.

Abstract

Reconstructing a dynamic object with affine motion in computerized tomography (CT) leads to motion artifacts if the motion is not taken into account. In most cases, the actual motion is neither known nor can be determined easily. As a consequence, the respective model that describes CT is incomplete. The iterative RESESOP-Kaczmarz method can - under certain conditions and by exploiting the modeling error - reconstruct dynamic objects at different time points even if the exact motion is unknown. However, the method is very time-consuming. To speed the reconstruction process up and obtain better results, we combine the following three steps: 1. RESESOP-Kacmarz with only a few iterations is implemented to reconstruct the object at different time points. 2. The motion is estimated via landmark detection, e.g. using deep learning. 3. The estimated motion is integrated into the reconstruction process, allowing the use of dynamic filtered backprojection. We give a short review of all methods involved and present numerical results as a proof of principle.

Dynamic computerized tomography using inexact models and motion estimation

TL;DR

The iterative RESESOP-Kaczmarz method can - under certain conditions and by exploiting the modeling error - reconstruct dynamic objects at different time points even if the exact motion is unknown, however, the method is very time-consuming.

Abstract

Reconstructing a dynamic object with affine motion in computerized tomography (CT) leads to motion artifacts if the motion is not taken into account. In most cases, the actual motion is neither known nor can be determined easily. As a consequence, the respective model that describes CT is incomplete. The iterative RESESOP-Kaczmarz method can - under certain conditions and by exploiting the modeling error - reconstruct dynamic objects at different time points even if the exact motion is unknown. However, the method is very time-consuming. To speed the reconstruction process up and obtain better results, we combine the following three steps: 1. RESESOP-Kacmarz with only a few iterations is implemented to reconstruct the object at different time points. 2. The motion is estimated via landmark detection, e.g. using deep learning. 3. The estimated motion is integrated into the reconstruction process, allowing the use of dynamic filtered backprojection. We give a short review of all methods involved and present numerical results as a proof of principle.
Paper Structure (10 sections, 6 theorems, 40 equations, 9 figures)

This paper contains 10 sections, 6 theorems, 40 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. RESESOP-Kaczmarz
  4. Motion Estimation via Landmark Detection
  5. Data-driven landmark detection
  6. Dynamic Filtered Backprojection
  7. Numerical Results
  8. Simulated Data
  9. Real Data
  10. Conclusion

Key Result

Lemma 2.4

(Calculation of projection onto intersection of hyperplanes) \newlabellem:projectionIntersection Let $H = \bigcap_{i = 1}^{n} H(u_i,\alpha_i)$ be the intersection of hyperplanes for $u_i \in X$ and $\alpha_i \in \mathbb{R}$ for $i = \{1,\dots,n\}, n\in \mathbb{N}$. Then the projection of $f \in X$ where $\tilde{t} = (\tilde{t_1},\dots,\tilde{t_n})$ minimizes the function If the elements $u_1,\d

Figures (9)

  • Figure 1.1: Combined Method
  • Figure 2.1: CNN6 architecture
  • Figure 2.2: Pre-training (left) and training loss (right)
  • Figure 3.1: Landmark detection on reconstructions from RESESOP-Kaczmarz without noise
  • Figure 3.2: Shifted rectangle without noise
  • ...and 4 more figures

Theorems & Definitions (14)

  • Definition 2.1
  • Remark 2.3
  • Lemma 2.4
  • Remark 2.5
  • Theorem 2.7
  • Theorem 2.8
  • Definition 2.9
  • Remark 2.10
  • Definition 2.11
  • Lemma 2.12
  • ...and 4 more