GE Maxxus 3D Reconstruction Simulation Results

This page presents an illustrative comparison of SSRB/2D-FBP reconstruction versus 3D-PLS (penalized least-squares) reconstruction of 3D PET data. The projection data was simulated according to the geometry of the GE Maxxus dual-head coincidence imager being developed at the University of Washington by Tom Lewellen et al. Software may be available, contact J. Fessler.

The geometry is a pair of rectangular Anger cameras (508mm transaxial by 340mm axial) separated by 626mm, for a maximum acceptance angle of about 28 degrees. The sampling was 64 transaxial bins by 42 axial bins (7.9mm spacing), with 17 polar angles and 50 azimuthal angles. A 3M count emission scan was simulated of an elliptical phantom with 4 hot spheres. Uniform attenuation within the ellipse was included, and 20\% random coincidences were added, but no scatter was modeled. The image volumes were reconstructed on a 64 by 64 by 32 grid.

The images below show 6 of the 32 reconstructed slices. The 1st row is the true phantom. The 2nd row is the SSRB/2D-FBP reconstructions (5 of the 17 polar angles were averaged together). The 3rd row is the 3D-PLS reconstructions using 3 iterations of the conjugate-gradient (CG) algorithm with no preconditioner. The 4th row is the 3D-PLS reconstructions using 10 iterations of the conjugate-gradient (CG) algorithm with no preconditioner. The CG algorithm was initialized with the SSRB/2D-FBP images.

The 3D-PLS images appear to have lower noise and higher spatial resolution.

Three iterations of the CG algorithm required 56 seconds on a DEC AlphaStation 600/5-333. The software has been tested on an IBM SP-2 parallel computer and speedup factors of over 90% are typical for up to 8 processors, so this method is very well suited to coarse-grain parallelization.

Currently the algorithm uses an on-the-fly forward and backprojector, so only about 3Mbyte of RAM was required for the above reconstructions.

There is negligible difference between the 3 and 10 iteration 3D-PLS-CG images. This agrees with other reports that iterative algorithms can converge very quickly for 3D PET. Proper preconditioning should lead to even faster convergence.

GE Maxxus 3D Reconstruction Results

As Les Rogers says, simulations are doomed to succeed. Here is the corresponding comparison from real data, courtesy of the University of Washington PET group led by Tom Lewellen with the support of GE Medical.

The top row is SSRB/2D-FBP, the bottom row is 10 iterations of 3D-PLS-CG. This data has scatter, randoms, and attenuation, none of which has been corrected in either reconstruction.

Note that all of the above is unweighted penalized least squares. What I'd rather be showing is penalized weighted least squares, but that requires a modified penalty function that is currently under development. It is probably a secondary effect relative to randoms, scatter, and attenuation correction for this data though...

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