, Xiaoyi Jiang1, Mohammad Dawood2 and Klaus P. Schäfers2
(1)
Department of Mathematics and Computer Science, University of Münster, Münster, Germany
(2)
European Institute for Molecular Imaging, University of Münster, Münster, Germany
In the previous chapter we have seen tailored methods for the estimation of motion between gates representing different motion states. Based on this knowledge, we eliminate motion induced image artifacts in a subsequent correction step. In this chapter, we give an overview of strategies for motion correction. The presented correction techniques vary between methods which rely on already available motion information (e.g., averaging) and methods that incorporate motion estimation into the correction procedure (e.g., joint reconstruction of image and motion). In this context, we particularly introduce advanced motion correction pipelines for dual gated PET which efficiently combine motion estimation and elimination.
3.1 Motion Correction Strategies
We already introduced the basic concept of motion correction in Sect. 1.5, focusing mainly on motion correction schemes based on gating with subsequent motion estimation and correction. A more detailed discussion on these approaches is given in the following.
To reduce motion and its impact on further analysis in thoracic PET, several approaches were proposed recently. Unlike the more sophisticated approaches that try to estimate motion and subsequently correct for it, optimized gating approaches have recently been introduced in clinical diagnostics, called optimal gating. Almost all other approaches have in common that motion is estimated on the basis of PET data instead of, e.g., gated CT images, in order to keep the radiation burden as low as possible. They can be classified into the four groups introduced in Sect. 1.5.1 plus the optimal gating strategy:
1.
Optimal gating
2.
Averaging of aligned images
3.
Motion compensated re-reconstruction
4.
Event rebinning
5.
Joint reconstruction of image and motion
3.1.1 Optimal Gating
In contrast to cardiac motion induced by myocardial contraction, respiratory motion has a quite irregular pattern. Most of the time, the thorax is resting at the expiration phase, whereas the inspiration phase is often relatively short. Recently, a new amplitude-based gating approach, called optimal gating, was introduced by van Elmpt et al. [131] that defines the maximum time phase at end-expiration where the motion is minimal. Therefore, a histogram is formed of the respiratory signals, acquired during the list mode PET scan, and converted to a cumulative distribution function. On this function, a lower and upper level is determined that forces the total sensitivity to equal to a certain percentage (e.g., 35 %) of the acquired breathing signals. This percentage is called the optimal gating yield.
Although most of the acquired data (e.g., 65 %) is discarded in performing optimal gating leading to noisier images, this approach provides a robust method of motion reduction. It could be demonstrated that optimal gating is a user-friendly respiratory gating method to increase detectability and quantification of upper abdominal lesions compared to conventional acquisition techniques [130].
3.1.2 Averaging of Aligned Images
After gating the acquired PET data, each gate is reconstructed individually and aligned to one designated reference gate. To overcome the problem of low SNRs, the aligned images are averaged (summed) afterwards. In the context of respiratory motion correction, Dawood et al. [34] propose an optical flow based approach and Bai et al. [6–8] use a regularized B-spline approach with a Markov random field regularizer. In the context of cardiac motion correction, Klein et al. [73, 75] propose a technique using 3D optical flow and model the myocardium as an elastic membrane. In their approach intensity modulations caused by cardiac motion (see Sect. 2.1.4) are not addressed. The averaging of aligned images is described in more detail in Sect. 3.2.1 of this book.
3.1.3 Motion Compensated Re-reconstruction
Similar to the averaging approach, gating is applied and each individually reconstructed gate is aligned to one assigned reference gate. The obtained motion information is incorporated into a subsequent re-reconstruction of the whole data set. The lines of response are adjusted according to the motion field which implies time-varying system matrices, see [46, 80, 111, 112] for respiratory motion correction approaches. Motion compensated re-reconstruction is also used in Sect. 3.2.3 in connection with the simplified motion correction pipeline.
3.1.4 Event Rebinning
The acquired list mode data is gated and each gate is reconstructed. Motion is estimated based on these reconstructed images. The initial list mode data is rebinned in a subsequent step by applying the transformation gained from the motion estimation step [79]. As only affine transformations are allowed, such methods can correct for respiratory motion (which is primarily locally rigid) to a certain extent but not for non-linear cardiac motion.
3.1.5 Joint Reconstruction of Image and Motion
In joint reconstruction, motion is estimated simultaneously to the reconstruction of the image [13, 14, 20, 68, 89, 121]. An objective function is optimized in two arguments: image and motion. Hence, only one image with the full statistics is reconstructed. A drawback of these approaches is the relatively high computational cost.
3.2 Motion Correction Pipelines for Dual Gated PET
As we have seen with the motion correction approaches discussed so far, motion is typically estimated between each gate and a certain reference gate (based on the motion estimation methods presented in Chap. 2) and eliminated subsequently in a gate-by-gate manner. This intuitive motion correction procedure is further described with the serial pipeline in Sect. 3.2.1 specifically for dual gated PET. However, dual gated PET offers more advanced opportunities for the correction step. In Sects. 3.2.2 and 3.2.3 we present pipelines for motion correction which efficiently combine motion estimation and motion correction. The key feature is thereby the decoupling of respiratory and cardiac motion. This means that respiratory and cardiac motion are estimated separately with intermediate correction steps. As a result, the presented simplified pipelines feature a reduced number of motion estimation steps with an increased robustness towards noise in each step.
3.2.1 Serial Pipeline
The core idea of the serial pipeline for motion correction in dual gated PET, as proposed in [51], is a sequential execution of the motion estimation and motion correction step. First, the whole m × n matrix of m respiratory and n cardiac images is built. The m × n matrix consists of the individual reconstructions of all dual PET gates. An example of a dual gating image matrix is given in Fig. 1.7. After choosing a particular reference phase, each of the m ⋅ n − 1 remaining (template) images is registered to this reference phase with the methods described in Chap. 2. The motion correction step is performed by means of a subsequent averaging of the transformed (i.e., motion corrected) gates. In summary, this serial pipeline consists of the following steps:
1.
Determination of the dual gating signal
2.
Reconstruction of all dual gates (m ⋅ n resulting images)
3.
Dual motion estimation (m ⋅ n − 1 registration tasks)
4.
Averaging of all motion corrected dual gates (1 resulting image)
The steps of the serial pipeline are visualized in Fig. 3.1. This schematic illustration facilitates a comparison to the pipelines presented in the remainder of this chapter, cf. Figs. 3.2 and 3.3.
Fig. 3.1
Schematic illustration of the serial pipeline. All dual gates are reconstructed and used for a gate-by-gate motion estimation. Classic reconstructions are used with a final averaging of the image-based motion corrected gates
Fig. 3.2
Schematic illustration of the simplified pipeline [119]. The dual motion is decomposed into its respiratory and cardiac component. Classic reconstructions are used with a final averaging of the image-based motion corrected gates
Fig. 3.3
Schematic illustration of the simplified pipeline with MCIRs [54]. The classic reconstructions of the simplified pipeline are replaced by MCIRs. The reconstruction of all single dual gates is no longer necessary
A positive property of the serial pipeline is the easy and straightforward implementation which is consequently not very error-prone. But since all dual gates need to be actually reconstructed, the fineness of the subdivision due to the dual gating is limited in practice (i.e., m and n need to be chosen rather small) as the noise level for the images used for registration is increased. This in turn results in a reduced compensation of the motion induced artifacts.
3.2.2 Simplified Pipeline
The serial pipeline in Sect. 3.2.1 requires many registration steps operating on the individual noisy dual gates. We propose a simplified pipeline for cardiac PET motion correction based on our previous work in [119] to reduce the m ⋅ n − 1 motion estimation steps which are necessary in the serial approach. The main idea of the simplified pipeline is to decouple respiratory and cardiac motion estimation. Instead of matching all m ⋅ n − 1 gates to an assigned reference gate, only m − 1 respiratory matching steps with subsequent n − 1 cardiac matching steps are performed.
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