Introduction In projection reconstruction (PR) MRimaging, k-space is sampled along straight-line con-tours through the origin. By the central-slice theorem,the values along each contour represent the 1-D FT ofthe projection of the final image in the direction normalto that contour. Image-space projections computed fromthe k-space data can thus be reconstructed using anyavailable reconstruction tool.

A powerful property of the PR approach is itsperformance in the face of angular undersampling. Thestep size between angles specifies the radius of a reducedFOV. Focal objects entirely contained within that FOVare reconstructed with full resolution. Furthermore, ob-jects outside this reduced field are not misplaced intothis field as a consequence of undersampling as they arein other acquisition approaches. These properties havespawned interest in the possibility that PR approachesoffer considerable reductions of acquisition time for thesame image quality. Realizing this advantage has beenlimited to date by the fact that each focal object in thetotal FOV, while ideally reconstructed itself, introducesartifacts that fall outside the reduced FOV centered onthat object. Each point in the image thus representsboth the ideal reconstruction of the objects within thereduced FOV centered at that site plus the artifacts con-tributed by all the other objects located outside that re-duced FOV. Although these artifacts are often tolerable,their elimination remains one of the important openquestions in undersampled PR imaging.

It is our hypothesis that these artifacts arise fromthe conventional use of analytic reconstruction methodssuch as filtered back projection (FBP). FBP assumesperfect projection data, and offers no means of adaptingto projection noise, missing projection data, or projec-tion undersampling. These have been accommodatedin other projection imaging contexts by iterative recon-struction techniques, with considerable success. Pro-jections of a trial model image matrix are compared tothe available measured data, and the trial matrix is modi-fied on the basis of the observed discrepancies. The re-sulting modified matrix is then the input to the next it-eration. The estimation-maximization (EM) approachto the modification process [1] is known to converge tothe maximum likelihood solution in the event of Pois-son-distributed projection data. Iterative approachessuch as EM may offer total control of undersamplingartifacts without loss of image quality.

Materials and Methods Femoral artery MRA wasperformed in a normal subject as previously reported[2]. A 3D projection acquisition sequence employed400 fractional echo readouts distributed over 180° in thex-y plane and Fourier encoding in the slice direction.Every fourth angle was selected to create an undersam-pled data set, which was reconstructed using both FBPand the EM method implemented in the IDL language.The ordered-subset refinement of the algorithm (3) wasused. In this refinement, the trial matrix is updated sev-eral times within each iteration, rather than once, on thebasis of a subset of the available angles. Subsets arechosen and ordered such that the changes effected byeach update are maximal, increasing the rate of conver-gence. The 100 angles were divided into 10 subsets, and

the reconstruction was allowed to proceed for 12 itera-tions.

Results Figure 1 compares the 512x512 reconstruc-tions of a single coronal slice from the femoral arterystudy. FBP results for both 400 (a) and 100 (b) anglesare shown. The result with 100 angles is also presentedwith window parameters set to demonstrate the under-sampling artifacts (c). These are compared to the itera-tive reconstruction (d) of the same 100 angle data set,displayed with the same window parameters as (c).

Figure 1.Discussion Iterative reconstruction of undersampledPR data greatly reduced the artifacts seen in FBP recon-struction without compromising other aspects of imagequality. EM performed well despite the non-Poissonnature of the projection data. Adaptation of EM to theknown statistics of MR projections is underway in ourlab. This advance brings closer the promise of PR im-aging with angular undersampling to provide reducedacquisition time for the same resolution, or increasedresolution for the same acquisition time.

Acknowledgements This work was supported bygrant 1R01-HL62425, National Institutes of Health.

References1. Dempster AP, et al., J. Roy. Stat. Soc. B, 39, 1-38,1977.2. Peters DC, et al., Proc. Eightth ISMRM,, 153, 1998.3. Hudson HM and Larkin RS, IEEE Trans. Med. Imag. 4,601-9, 1994.

Control of Angular Undersampling Artifacts in Projection-based MR Angiography by Iterative Reconstruction

James E. Holden, Orhan Unal, Dana C. Peters, Terence R. OakesDepartments of Medical Physics, Radiology, Physics, and Pschology, University of Wisconsin-Madison

Madison, WI, 53792-3252 USA

� �

� �