### Abstract

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

Original language | English (US) |
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Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Volume | 7961 |

DOIs | |

State | Published - 2011 |

Event | Medical Imaging 2011: Physics of Medical Imaging - Lake Buena Vista, FL, United States Duration: Feb 13 2011 → Feb 17 2011 |

### Other

Other | Medical Imaging 2011: Physics of Medical Imaging |
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Country | United States |

City | Lake Buena Vista, FL |

Period | 2/13/11 → 2/17/11 |

### Keywords

- graphics processing unit
- Iterative image reconstruction
- sparse matrix factorization
- system modeling

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Electronic, Optical and Magnetic Materials
- Biomaterials
- Radiology Nuclear Medicine and imaging

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## Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 7961). [79610K] https://doi.org/10.1117/12.878799