• Keine Ergebnisse gefunden

This chapter introduces a general methodology for motion estimation and compen-sation in tomography. In particular, a solution is provided to estimate the motion in-formation for the class of dein-formations that can be described by a strictly increasing bijective mapping function in projection space. Tackling these specific deformations is inspired by the complementary work of Desbat et al., showing that exact recon-struction from inconsistent projections and a motion description, is still possible for this class of deformations.

The extraction of the motion information is based on numerical integration, without using any prior knowledge about the temporal or spatial smoothness of the underlying displacement field. This is a simple non-iterative elastic signal registra-tion procedure that can be computed in a single pass over the input data. The proposed iterative motion correction framework can be seen as a generalization of a conventional FBP image reconstruction. Indeed, if no motion corrupts the pro-jections, the process converges in one iteration and reduces to a standard image reconstruction.

6

Local Motion Correction

in 3D Parallel-Beam Geometry

T

his chapter extends the technique described previously and presents a new iterative motion correction technique composed of motion estimation in pro-jection space,motion segmentation in image space andmotion compensation within an analytical filtered-backprojection (FBP) image reconstruction algorithm. The motion is estimated by elastic registration of acquired projections on reference pro-jections, sampled from the image reconstructed in a previous iteration step. To apply the motion compensation locally, the image regions significantly affected by motion are also segmented.

First the perceived motion is identified in projection space by computing the absolute difference betweenacquired line integrals andreferenceline integrals. Then, differences are reconstructed in image space and the image is regularized with a pipeline of standard image processing operators. The result of the segmentation is a normalized motion map, associating each image element with an estimate of the relative amplitude of the detected motion. The estimated displacement vectors in projection space and the reconstructed motion map in image space are then used by an adaptive motion-compensated FBP algorithm to reconstruct a sharper image.

This work has been presented at the SPIE Medical Imaging Conference organized at Lake Buena Vista, USA, on the February 7–12 of 2009 (Schretteret al., 2009b).

6.1 Introduction

The estimation of organ motion from X-ray projections is an ill-posed problem by nature. Since the projections are two-dimensional while the image space is three-dimensional, the system is undetermined if one wants to extract the 4D information of motion along time given the 3D information of projections acquired from a dy-namic object (Grangeatet al., 2002;Bonnet et al., 2003).

It is mandatory to augment the input information to solve the motion estimation problem. Often, the assumption is made that the organ motion is smooth and periodic. Under those hypotheses, gating the projection data with the respiratory signal allows independent reconstructions of each frame of a dynamic sequence of volumetric images (Sonkeet al., 2005;Yanget al., 2008). Furthermore, the motion

can be estimated with fair accuracy, by image registration of successive reconstructed volumes Isolaet al. (2008).

The approach of this work follows the proposal of Roux et al.(2004); Desbat et al.(2006, 2007b). Desbat assumes that for any given time, the displacement vec-tors are identical for all points on a same X-ray projection ray and that these vecvec-tors are orthogonal to that line. It is easy to see that displacement along projection lines does not modify the value of line integrals (Milanfar, 1999). Hence, the measured intensities are invariant to the orthogonal component of the displacement vectors.

Those motion components can not be perceived in X-ray projections and therefore do not yield any data inconsistency (Yu et al., 2006; Yu and Wang, 2007).

Constraining the displacements to be orthogonal to line integrals yields exact im-age reconstruction algorithms. Therefore, this assumption does not lead to any loss of generality since the reconstruction reduces to a standard filtered-backprojection (FBP) (Kak and Slaney, 1988; Turbell, 2001) if the displacement magnitudes are set to zero. However, it is likely that patient motion will not fulfill the conditions of the admissible class of deformations mentioned above. For instance, an incorrect motion estimate could corrupt the static parts of the image. By introducing the concept oflocal motion compensation, the admissible class of motion is extended in this work to capture also some deformations that bend integration lines into curves in image space.

The rationale of the method presented in this chapter is the combination of an iterative estimation of the perceived patient motion in projection space and a heuristic segmentation of the image region where organ motion is detected. The deformation estimate and the motion segmentation provide additional information that are used by a motion-compensated FBP algorithm to reconstruct a sharp static image from the acquired projection data. This technique has already demonstrated promising results for the estimation of affine motion from projections of a deforming Shepp-Logan phantom (Schretter et al., 2008).

The remainder of this chapter is structured as follows. The extended iterative motion correction method is described in section 6.2 in the context of volumetric im-age reconstruction. The motion correction problem is split into three complementary sub-problems: motion estimation, motion segmentation and motion compensation.

Results are shown qualitatively and quantitatively in section 6.3, for reconstructions from realistic projections simulated from clinical patient data. Since the method does not assume any periodicity of the motion model, it can correct artifacts due to unstructured patient motion, such as breath-hold failure, abdominal contractions, and nervous movements. Finally, conclusions are drawn in section 6.4.