# EMrecon: An Expectation Maximization Based Image

Reconstruction Framework for Emission Tomography Data

Thomas Kösters^{1}^{,2}, Klaus Schäfers^{1}, and Frank Wübbeling^{2}

^{1} European Institute for Molecular Imaging (EIMI), University of Münster, Germany

^{2} Institute for Computational and Applied Mathematics, University of Münster, Germany

## The Software Package

The EMrecon (Expectation Maximization RECONstruction) project was initiated in 2006 to have an own / free implementation of classical iterative reconstruction algorithms for the wire-chamber based quadHIDAC small animal PET scanner. Since no other available software package (except for a closed source implementation, written by the group of Andrew Reader) could handle this special kind of data, it was inevitable to create a new reconstruction framework in order to develop and validate new correction methods for attenuation, scatter or motion.

Started as a reconstruction tool for quadHIDAC data only, EMrecon was extended to support other scanner geometries as well. Now PET scanners with block crystal geometry can easily be added using a simple syntax similar to the scanner definitions in the GATE simulation framework. EMrecon was succesfull tested with cylindrical scanner geometries like the Siemens Inveon Small Animal PET or the Siemens Biograph mMR. In addition spherical scanner geometries as used in the Siemens Biograph Sensation 16 located at the University Hospital at Münster are supported.

**Transversal view on the geometry of a hypothetical crystal PET scanner with XCAT emission and attenuation map. Red crystals indicate the filled gaps.**

**Forward projection from image space into data space to generate artificial data. The diamond patterns result from gaps between crystal blocks.**

**The missing bins in the sinogram can be filled, e.g. using a forward projection of reconstructed data.**

All reconstruction algorithms included (so far) in EMrecon are based on the expectation maximization (EM) and ordered subset expectation maximization (OSEM) algorithms. Several modifications were created to tackle different problems, like motion correction during reconstruction, combined motion estimation, motion correction and reconstruction or more-dimensional reconstruction approaches. The code of all algorithms is parallelized for shared-memory systems. To speed up the more complex algorithms, the C-code was ported to different platforms, like Cluster, GPUs etc. Reconstructions may be performed directly from listmode data or from sinograms / michelograms.

Next to the reconstruction of different datatypes, a toolbox for EMrecon was developed to perform corrections on the data before reconstruction, like attenuation correction and scatter correction. In addition listmode data may be sorted into sinograms or if a gating signal is provided also into different sinograms depending on the number of defined gates.

## Contact

Interested in using EMrecon? Please contact thomas.koesters@nyumc.org. Since not all modifications have been published so far and due to restrictions on publishing information given by the scanner manufacturer, some of the presented algorithms are not included in the public release.

## References

**T. Kösters**, **K. P. Schäfers**, and **F. Wübbeling**: EMrecon: An Expectation Maximization Based Image Reconstruction Framework for Emission Tomography Data. In NSS/MIC Conference Record, IEEE, 2011, pp. 4365-4368.

**T. Kösters**: Derivation and Analysis of Scatter Correction Algorithms for Quantitative Positron Emission Tomography. In Ph.D. Thesis, Universität Münster, 2010.

M. Fieseler, **T. Kösters**, F. Gigengack, H. Braun, H. H. Quick, **K. P. Schäfers** and X. Jiang: Motion Correction in PET-MRI: A Human Torso Phantom Study. In NSS/MIC Conference Record, IEEE, 2011, pp. 3586-3588.

A. Konik, **T. Kösters**, M. T. Madsen, and J. J. Sunderland: Evaluation of Attenuation and Scatter Correction Requirements as a Function of Object Size in Small Animal PET Imaging. In Transactions on Nuclear Science, IEEE, 2011, vol. 58, no. 5, pp. 2308-2314.

J. Müller, C. Brune, **F. Wübbeling**, A. Sawatzky, **T. Kösters**, **K. P. Schäfers** and M. Burger: Reconstruction of Short Time PET Scans Using Bregman Iterations. In NSS/MIC Conference Record, IEEE, 2011, pp. 2383-2385.

M. Dawood, **T. Kösters**, M. Fieseler, F. Büther, X. Jiang, **F. Wübbeling** and **K. P. Schäfers**: Motion Correction in Respiratory Gated Cardiac PET/CT a Using Multi-Scale Optical Flow. In Proceedings of the MICCAI 2008, LNCS, vol. 5242, 2008, pp. 155-162.

A. Sawatzky, C. Brune, **F. Wübbeling**, **T. Kösters**, **K. P. Schäfers**, and M. Burger: Accurate EM-TV Algorithm in PET With Low SNR. In NSS/MIC Conference Record, IEEE, 2008, pp. 5133-5137.

M. Benning, **T. Kösters**, **F. Wübbeling**, **K. P. Schäfers**, and M. Burger: A Nonlinear Variational Method for Improved Quantification of Myocardial Blood Flow Using Dynamic H2O15 PET. In NSS/MIC Conference Record, IEEE, 2008, pp. 4472-4477.

M. Schellmann, S. Gorlatch, D. Meiländer, **T. Kösters**, **K. P. Schäfers**, **F. Wübbeling**, and M. Burger: Parallel Medical Image Reconstruction: From Graphics Processors to Grids. In Parallel Computing Technologies, ser. Lecture Notes in Computer Science, V. Malyshkin, Ed. Springer Berlin / Heidelberg, 2009, vol. 5698, pp. 457-473.