期刊
IEEE TRANSACTIONS ON IMAGE PROCESSING
卷 23, 期 4, 页码 1678-1693出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2014.2305840
关键词
Computed tomography; energy-sensitive X-ray computed tomography; spectral CT; multienergy CT; photon counting detectors; low-rank modeling; spectral regularization; tensor rank; inverse problems; iterative reconstruction; T-SVD; tensor decomposition
资金
- National Science Foundation [NSF DMS 0914957]
- U.S. Department of Homeland Security [2008-ST-061-ED0001]
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a tensor-based iterative algorithm that simultaneously reconstructs the X-ray attenuation distribution for each energy. We use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor-based regularizers. In particular, we model the multispectral unknown as a three-way tensor where the first two dimensions are space and the third dimension is energy. This approach allows for the design of tensor nuclear norm regularizers, which like its 2D counterpart, is a convex function of the multispectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach. Simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective (spectral) computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent.
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