Abstract:An inverse problem is called dynamic if the object changes during the data acquisition process. This occurs e.g. in medical applications when fast moving organs like the lungs or the heart are imaged. Most regularization methods are based on the assumption that the object is static during the measuring procedure. Hence, their application in the dynamic case often leads to serious motion artefacts in the reconstruction. Therefore, an algorithm has to take into account the temporal changes of the investigated ob… Show more
“…If the motion is known, it can be possible to reconstruct consistent 3d representations from the inconsistent projections. Tomographic reconstruction with known motion has been investigated in the literature 1,10–12 and schemes have shown success in the context of medical CT (heart beat, breathing) 13–17 , however, either for pre-determined motion or for rather sparse objects and over-sampled images. Typically, in such applications the resolution is much smaller than the voxel size, and image artefacts are more deteriorating than loss of resolution.Figure 1Illustration of artefacts induced by motion and dynamic processes during a tomographic measurement.…”
We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.
“…If the motion is known, it can be possible to reconstruct consistent 3d representations from the inconsistent projections. Tomographic reconstruction with known motion has been investigated in the literature 1,10–12 and schemes have shown success in the context of medical CT (heart beat, breathing) 13–17 , however, either for pre-determined motion or for rather sparse objects and over-sampled images. Typically, in such applications the resolution is much smaller than the voxel size, and image artefacts are more deteriorating than loss of resolution.Figure 1Illustration of artefacts induced by motion and dynamic processes during a tomographic measurement.…”
We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.
“…Within each subset, where the object does not change, a reconstruction is performed. Finally, if the motion is known upfront, it is possible to compensate for the motion of the object in the CT-scanning Hahn (2014) by using the method of the approximate inverse Louis (1996).…”
Computed Tomography is a powerful imaging technique that allows non-destructive visualization of the interior of physical objects in different scientific areas. In traditional reconstruction techniques the object of interest is mostly considered to be static, which gives artefacts if the object is moving during the data acquisition. In this paper we present a method that, given only scan results of multiple successive scans, can estimate the motion and correct the CT-images for this motion assuming that the motion field is smooth over the complete domain using optical flow. The proposed method is validated on simulated scan data. The main contribution is that we show we can use the optical flow technique from imaging to correct CT-scan images for motion.
“…Analytic techniques for reconstruction of dynamic objects, known as motion compensation, have been used widely for different types of motion, like affine deformation, see e.g. 5,6,12,13,18,20,21,26 [5,6,12,13,18,20,21,26]. In the case of non-affine deformations, there is no inversion formula.…”
Section: Introductionmentioning
confidence: 99%
“…In a recent work, Hahn and Quinto 11 [11] studied the dynamic operator which allows us to study the original dynamic problem with a more general set of curves (see also 7 [7],) and then transfer the result to a dynamic operator A given by ( 1.1 1.1). The dynamic operator A formulated as above falls into the general microlocal framework studied by Beylkin 1 [1] (see also 13 [13]) which goes back to Guillemin and Sternberg 9, 10 [9,10] who studied the integral geometry problems with a more general platform from the microlocal point of view. See also 7 [7], where a weighted integral transform has been studied on a compact manifold with a boundary over a general set of curves (a smooth family of curves passing through every point in every direction).…”
Let X be an open subset of R 2 . We study the dynamic operator, A, integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered, as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to Fan beam geometry.with a smooth motion where the limited data case has been analyzed, and characterization of visible and added singularities have been investigated. Our work in this paper is motivated by these dynamic measurements. We first show this dynamic problem can be reduced to an integral geometry problem integrating over level curves. By an appropriate change of variable (see section 2), A can be written asTherefore, we study the following general operator:Af (s, t) = φ(t,x)=s µ(t, x)f (x)dS s,t ,
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