Motion Evoked Artifact DeconvolutionBrian E. Nett1, Jang Hwan Cho 2, and Jed D. Pack 3

1 GE Healthcare, 3000 N. Grandview Blvd., W-1180, Waukesha WI , USA2 Endra, Inc, 3600 Green Ct #350, Ann Arbor, MI , USA

3 GE Global Research Center, One Research Circle, Niskayuna, NY USA,

I. INTRODUCTION

In computed tomography (CT) reconstruction the imagefunction to be reconstructed, f(x, y, z), is generally as-sumed to be stationary during the acquisition. When thisassumption is violated motion artifacts become apparent inthe reconstructed images due to the inconsistency betweenprojections as the image function is really a function oftime as well, f(x, y, z, t). Motion compensation techniqueshave been developed which make an estimate of the timedependent changes and account for these changes in thereconstruction. Several such approaches have been developedin the literature. One specific implementation of a motionestimation and correction algorithm is the SnapShot Freeze(SSF) algorithm from GE Healthcare [1]. The SSF algorithmuses three reconstructed image volumes as input: identifiesthe coronary arteries, estimates the motion in the coronaryarteries and compensates for the motion near the coronaryarteries. In this work we present a straightforward methodwhich may be used in conjuction with a vessel specificmotion estimation and compensation approach. The aim of thisalgorithm is to reduce the residual motion artifacts adjacentto the cardiac chambers. These artifacts are caused by thefact that the chambers (e.g. the left ventricle (LV)) maydeform rapidly during the acquisition. Since the contrast inthe LV is much greater than the surrounding myocardium theseinconsistencies can lead to false hyper-attenuation and hypo-attenuation in the myocardium. The technique proposed hereaims to mitigate these errors by correcting for the change inthe contrast enhanced region throughout the scan. This methodis termed Motion Evoked Artifact Deconvolution (MEAD), asthis approach is analogous to a deconvolution operation. In thecase of cardiac imaging MEAD may be applied in combinationwith targeted motion estimation and compensation processingsuch that the images will have been corrected in both thevessels and the myocardium. MEAD is also computationallyinexpensive compared with fully iterative techniques aimed atsolving the same problem.

II. METHODS

A. Algorithm Description

This algorithm has been developed in a general mannerand may apply to a variety of areas where motion artifactsexist. Since the primary motivation of this work is for cardiacimaging we use cardiac specific terminology below. However,one may directly substitute the contrast filled myocardium

with any other image feature that generates artifacts in theneighboring tissue due to significant differences in attenuationvalues. The primary goal of this algorithm in this specificcontext is to correct for the areas of false hyper-attenuationand hypo-attenuation in the myocardium which are causedby changes in the contrast throughout the acquisition timewindow. In this section we provide a description of thealgorithm. We first begin by defining several variables thatwill be used throughout the description. For simplicity thedependent variables are suppressed.

• ΦN - the phase corresponding to a given set of data, (i.e.the center phase) of that data

• N - integer number, corresponds to the prescribed phase,where (2 ·N − 1) total phases are used

• y - projection data• ymeas - measured projection data, assumed to be pre-

processed• f - image data• F - Fourier transform of the image data• R - Radon transform, more generally the forward x-ray

projection operator• R−1 - inverse Radon transform, more generally CT re-

construction such as FBP (Filtered-BackProjection) type,FBPD (Filtering the BackProjection of Differentiateddata) type or iterative reconstruction.

• FFT - Fast Fourier Transform• IFFT - Inverse Fast Fourier Transform• HT - Hard Thresholding operation• LP - Low Pass filter• con - contains only high contrast material such as iodi-

nated contrast and bone• residual - the difference between the reconstruction incor-

porating changing contrast and the reconstruction of thecontrast at one phase

• mead - the final output image, (Motion Evoked ArtifactDeconvolution)

The general flow for the algorithm is depicted in Figures1 and Figure 2. The assumption is that some contribution toartifacts in the myocardium is caused due to inconsistenciescaused by the change of shape of the highly attenuatingchamber, which is directly adjacent to the myocardium. Theseare the artifacts which this algorithm aims to address, andartifacts such as beam hardening are outside the current scope.This algorithm can be viewed simply as two steps: Step 1-create a forward model to reproduce the artifacts due to motion

The 4th International Conference on Image Formation in X-Ray Computed Tomography

565

of the chamber (Figure 1), Step 2- subtract the motion evokedartifacts from the initial image (Figure 2). This process isanalogous to a deconvolution of the artifacts caused by themotion of the contrast filled chamber.

We begin by explaining Step 1, where the forward model ofthe motion artifacts is created. Here the term forward modelshould not be confused with the forward projection operator;rather, the forward motion model is the generation of animage which simulates the motion artifacts. Starting from themeasured projection data multiple images are reconstructed atdifferent phases, assume here (2 · N − 1) total phases areused, where the image fΦN corresponds to the prescribedimage. After images are reconstructed at multiple phases ahard thresholding operation is applied to the images such thatthe only non-zero contributions in the image are above a givenHU (Hounsfield Unit) threshold. Thus after the thresholdingonly bone, injected contrast and foriegn material such asimplanted metal will have non-zero values. A possible varationnot demonstrated here would be to use multiple thresholdinglevels such that the values below a certain threshold would alsobe included. For the purpose of this description the abreviation(con) will be used here as in this case the thresholding isperformed with the aim of identifying the areas of highcontrast (con) relative to tissue and motion of these objectscan induce artifacts. A forward projection operation in thenative coordinates then may be used to estimate the projectionthrough the reconstruction at each phase. These projectionsmay then be combined using a smooth feathering weight forthe contributions from the basis images. Finally the imagemay be reconstructed using a standard image reconstructionalgorithm such as the Parker weighted FBP [2] (Figures 1).This image, f con

Φ1:Φ(2·N−1), will contain the motion artifacts

(hyper/hypo myocardial values) caused by inconsistencies inthe high contrast object throughout the scan. Given the knownrelationship between projections and Fourier space we can alsoformulate this method in frequency space. For parallel-beamtomography the Fourier Slice Theorem provides a direct linkbetween projection space and Fourier space. In the case ofcardiac imaging using third generation geometry the mappingwill not be exact as the Fourier Slice Theorem assumes thatparallel projections are used in the acquisition. The differencelies in the fact that there is a slight time shift between thetrue parallel projection and the rebinned fan-beam projection.However, since this is a fraction of the time of the scan we donot believe this approximation will limit to the performanceof this technique. Since the Fourier transform is significantlyfaster the forward projection in Figure 1 can be replacedwith FFT , the view angle based smooth weighting of theprojections is replaced with smoothing varying angular masksthat are multiplied by the FFT (where the angular masksapplied to neighboring basis images sum to unity), and theFBP reconstruction is replaced with the IFFT .

After obtaining the forward motion model, f conΦ1:Φ(2·N−1)

, weturn to Step 2 where we subtract the motion evoked artifactsfrom the original image. First the difference is taken betweenthe forward motion model and the high contrast only image

ymeas

R−1

fΦN... ...fΦ1

HT

fΦ(2·N−1)

f conΦN

f conΦ1

f conΦ(2·N−1)

R (FFT )

F conΦN

F conΦ1

F conΦ(2·N−1)

F conΦ1:Φ(2·N−1)

R−1 (IFFT )

f conΦ1:Φ(2·N−1)

Fig. 1. Schematic diagram of the MEAD algorithm operating in Fourierspace, where the description of each step is given in the main text.

f conΦN

f conΦ1:Φ(2·N−1) fresidual

ΦN- =

LP

f̃residualΦN

fΦN fmeadΦN

- =

Fig. 2. The schematic operation to calculate the residual artifact imagefresidualΦN

and subtract a filtered version of it from the original image fΦN.

corresponding to the prescribed phase. This result is referredto here as fresidual

ΦNand represents the artifacts evoked from

high contrast objects. In the case that N is much less thanthe number of acquired views a low pass filter is applied tothe residual to ensure that high frequency artifacts are notpropagated to the final image. This choice is re-enforced bythe knowledge that these motion evoked artifacts are low infrequency for clinically realistic motion of the high contrastobject.

This concludes the general description of the MEAD algo-rithm. An additional step which is taken for the cardiac datais to define a map in image space where SSF is performed.The SSF map has smooth transitions between the regionswhere SSF is applied and where no SSF corrections weremade. This mask is used such that the correction image,f̃residualΦN

, is set to zero within the region where SSF has beenapplied. In this manner the MEAD algorithm will not makeany contribution to the reconstruction of the coronary arteries.

The 4th International Conference on Image Formation in X-Ray Computed Tomography

566

This behavior is desired as the SSF algorithm provides superiorvessel correction as a true motion estimation and compensationalgorithm is required for the coronary vessels.

Note, also that this algorithm may be applied in an iterativemanner where the MEAD algorithm is applied to each of theinput phases, and then the MEAD algorithm is applied againusing the output from the first round of MEAD processing.

B. Input DatasetsThe initial evaluation of the algorithm is performed on

numerical phantoms and clinical scan data. The numericalphantom was generated from the XCAT anatomical and mo-tion mode [3] and the forward projections were generated withCatsim[4]. The sample data presented here corresponds to aheart rate of 55bpm. Clinical data was taken from a LightspeedVCT scanner with a gantry rotation period of 350ms. Theheart rate for the patient data presented here was in the rangeof 78-80 bpm during the acquisition. The reconstructions forthe clinical data were centered on 75% RR. The simulationdata was performed with axial acquisitions with a gantryrotation period of 280ms and the first clinical data were fromretrospectively gated helical scans. In Figure 3 we demonstrateeach of the intermediate steps needed to generate the forwardmotion model for a given slice in a clinical data set (Step1). After the forward motion model is computed it may beused in order to subtract the motion evoked artifacts (Step 2).For this same clinical case this procedure is demonstrated inFigure 4. The results were not found to be highly dependenton the threshold value used and a value of 200HU was usedfor results presented here.

III. RESULTS

Numerical phantom results are shown in Figure 5 andFigure 6. The images in Figure 5 correspond to an activephase in the motion cycle ( 50% RR). The upper row arethe images before and after the MEAD processing and thelower row are a subtraction from a reference image of thestatic XCAT phantom. Since the phase is not exactly matchedthe subtraction differences at the chamber boundaries areexpected, and one should focus on the myocardium regionin the subtraction images.

Several slices were chosen in uniform steps of 3.125mmin a clinical data set in order to demonstrate the effect ofthe MEAD processing on the reconstructed images. The firstset of images (Figure 7) was generated in slices where theopacified chamber displayed significant motion. In additionto the comparison of axial slices which are in the identicallocation, we have included reformatted images from the AW(Advantage Workstation) where other planes through the vol-umes are displayed. These planes are oriented along the shortaxis (Figure 8) of the heart rather than along the planes relativeto the scanner.

Finally, a demonstration of the possibility to perform mul-tiple iterations of MEAD processing is presented. In this caseMEAD was called for each of the input phases, thus MEADwas performed three times (i.e. the number of phases used) for

R−1

HT

FFT Comb

Fig. 3. The results of a slice from a clinical case processed with Step 1of the MEAD algorithm, where the forward model of the motion artifacts isgenerated. Note, that the format for this diagram matches that of Figure 1where the notation was introduced.

- =

LP

- =

Fig. 4. The results of a slice from a clinical case processed with Step 2 of theMEAD algorithm, where the residual from the forward model of the motionartifacts is subtracted from the original. Note, that the format for this diagrammatches that of Figure 2.

iteration 1 and one time for the second iteration. The resultsdemonstrate that significant improvement is possible for thesecond iteration of MEAD processing (Figure 9).

IV. CONCLUSIONS

An adjunct method was presented for vessel specific motionestimation and compensation algorithms, which aims to repro-duce motion artifacts in the myocardium and subtract these

The 4th International Conference on Image Formation in X-Ray Computed Tomography

567

FBP MEAD

|FBP-Static| |MEAD-Static|

Fig. 5. Example images from the active motion phase of the XCAT phantomdata before and after MEAD (upper row) [-200 200] HU, and the subractionfrom a static reference image (lower row) [0 50]HU.

11

3 4 5

2

XCAT ROIs

Fig. 6. Measurement results of the regions of interest (ROIs) in themyocardium for FBP and MEAD where the ROI locations are shown (upperpanel) and the values in the ROIs are plotted relative to the reference valuefor the stationary phantom. The error bars correspond to the std deviationwithin each ROI.

artifacts from the initial reconstruction. Results were presentedon phantom and clinical datasets.

REFERENCES

[1] B. Nett, J. Pack, and D. Okerlund, “Task based assessment of a motioncompensation algorithm via simulation of a moving stenotic vessel,” SPIEMedical Imaging., 2013.

[2] D. L. Parker, “Optimal short-scan convolution reconstruction for fan beamCT,” Med. Phys., vol. 9, pp. 254–257, 1982.

[3] W. Segars, M. Mahesh, T. Beck, E. Frey, and B. Tsui, “Realistic CTsimulation using the 4D XCAT phantom,” Med. Phys., 2008.

[4] B. DeMan, S. Basu, N. Chandra, B. Dunham, P. Edic, M. Iatrou,S. McOlash, P. Sainath, C. Shaughnessy, B. Tower, and E. Williams,“CatSim: a new computer assisted tomography simulation environment,”SPIE Medical Imaging, vol. 6510, p. 65102G, 2007.

FBP

FBP

SSF SSF+MEAD

SSF SSF+MEAD

FBP SSF SSF+MEAD

Fig. 7. Reconstruction results comparing the original image, the vesselcorrected SSF image and the SSF+MEAD correction image (HR=78-80 bpm).[-300 300]HU

SSF

SSF SSF+MEAD

SSF+MEAD

Fig. 8. Short axis reformats taken from a 3D workstation of approximatelythe same slices comparing SSF and SSF+ MEAD corrections. [-300 300]HU

SSF SSF+MEAD 1 Iteration SSF+MEAD 2 Iterations

Fig. 9. Reconstruction results demonstrating the feasability of multipleiterations of MEAD processing. [-300 300]HU

The 4th International Conference on Image Formation in X-Ray Computed Tomography

568