Abstract
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Objectives Fast and efficient statistically based image reconstruction is highly demanded for state-of-art high-resolution PET scanners. The 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 computation cost. Here we propose a new approach to obtain sparse factorized system matrix that allows an efficient fully 3D reconstruction with fast and parallel GPU (graphics processing unit) implementation.
Methods We propose a sparse factorization technique to decompose an accurate system matrix into a product of sparse components. The sparsity of each component is controlled by a sparsity prior with an adjustable parameter. The resulting sparse factors require much less storage space than the original system matrix and thus allow efficient implement of forward and back projectors for iterative image reconstruction. Because of their relatively small size, they can be loaded into a GPU to take the advantage of GPU parallel capacity to further reduce image reconstruction time.
Results We simulated a microPET II scanner. Images were represented by 148×148×168 voxels of size 0.2×0.2×0.2875 mm3. A precomputed accurate system matrix takes about 8.5 Gbytes after compression with symmetries. By applying the sparse factorization, the resulting sparse factors take only 520 Mbytes, about 17 fold reduction in size. The computation cost of a forward and backward projections using the precomputed accurate system matrix is 760 seconds on a 4-core CPU with 4 parallel threads, while it only takes 5 seconds on a single GPU (NVIDIA Tesla C1060) with the sparse factors.
Conclusions The proposed sparse matrix factorization is a good method for the fast and efficient 3D PET image reconstruction. The quantitative accuracy of this method will be further evaluated