基于代数迭代的Mojette变换层析重建算法
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摘要
提出了一种基于代数迭代的Mojette变换层析重建算法。在确定最佳投影角度的基础上,结合传统层析技术中的乘性代数迭代算法进行重建。利用该算法对轴对称火焰进行了层析重建。数值模拟结果表明,与基于角的重建算法相比,该算法在噪声较大情况下的层析重建质量更好。
A Mojette transform tomographic reconstruction algorithm based on algebraic iteration is proposed. In the algorithm, the optimal projection angles are determined, and the multiplicative algebraic iterative algorithm in traditional tomography is adopted for reconstruction. The proposed algorithm is used to tomographic reconstruction of an axisymmetric flame. Numerical simulations show that, for the projections with high noise, the proposed algorithm has better reconstruction quality comparing with the Corner Based Inversion.
A Mojette transform tomographic reconstruction algorithm based on algebraic iteration is proposed. In the algorithm, the optimal projection angles are determined, and the multiplicative algebraic iterative algorithm in traditional tomography is adopted for reconstruction. The proposed algorithm is used to tomographic reconstruction of an axisymmetric flame. Numerical simulations show that, for the projections with high noise, the proposed algorithm has better reconstruction quality comparing with the Corner Based Inversion.
引文
[1] Denisova N, Tretyakov P, Tupikin A. Emission tomography in flame diagnostics[J]. Combustion and Flame, 2013, 160(3): 577-588.
[2] Wan X, Gao Y Q, He X D. Three-dimensional flame temperature field reconstruction with multi-wavelength radiation computed tomography[J]. Acta Optica Sinica, 2003, 23(9): 1099-1104. 万雄, 高益庆, 何兴道. 多光谱辐射层析重建三维火焰温度场[J]. 光学学报, 2003, 23(9): 1099-1104.
[3] Brisley P M, Lu G, Yan Y, et al. Three-dimensional temperature measurement of combustion flames using a single monochromatic CCD camera[J]. IEEE Transactions on Instrumentation and Measurement, 2005, 54(4): 1417-1421.
[4] Ishino Y, Ohiwa N. Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame[J]. JSME International Journal Series B, 2005, 48(1): 34-40.
[5] Floyd J, Geipel P, Kempf A M. Computedtomography of chemiluminescence (CTC): Instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame[J]. Combustion and Flame, 2011, 158(2): 376-391.
[6] Li X S, Ma L. Volumetric imaging of turbulent reactive flows at kHz based on computed tomography[J]. Optics Express, 2014, 22(4): 4768-4778.
[7] Wang J, Song Y, Li Z H, et al. Multi-directional 3D flame chemiluminescence tomography based on lens imaging[J]. Optics Letters, 2015, 40(7): 1231-1234.
[8] Katz M B, Gordon R. Questions of uniqueness and resolution in reconstruction from projections[J]. Physics Today, 1979, 32(12): 52-56.
[9] Guédon J P, Normand N. The Mojette transform: the first ten years[C]. International Conference on Discrete Geometry for Computer Imagery, 2005: 79-91.
[10] Ji W P, Shen L S. Mojette transform and its applications to image processing[J]. Measurement & Control Technology, 2007, 26(3): 68-71. 计文平, 沈兰荪. Mojette变换及其应用[J]. 测控技术, 2007, 26(3): 68-71.
[11] Fayad H, Guédon J P, Svalbe I, et al. Applying Mojette discrete Radon transforms to classical tomographic data[J]. Proceedings of SPIE, 2008, 6913: 69132S.
[12] Hou W, Zhang C S. Parallel-beam CT reconstruction based on mojette transform and compressed sensing[J]. International Journal of Computer and Electrical Engineering, 2013, 5(1): 83-87.
[13] Li M J. The study on computed tomography image reconstruction algorithm based on compressed sensing theory[D]. Dalian: Dalian University of Technology, 2015. 李梦婕. 基于压缩感知理论的计算机层析图像重建算法[D]. 大连: 大连理工大学, 2015.
[14] Servières M, Normand N, Guédon J P, et al. The Mojette transform: discrete angles for tomography[J]. Electronic Notes in Discrete Mathematics, 2005, 20: 587-606.
[15] Song Y, Zhang B, He A Z. A novel iterative algorithm for moiré tomography[J]. Acta Optica Sinica, 2006, 26(3): 367-372. 宋旸, 张斌, 贺安之. 一种新的叠栅层析迭代算法[J]. 光学学报, 2006, 26(3): 367-372.
[16] Recur B, der Sarkissian H, Servières M, et al. Validation of Mojette reconstruction from Radon acquisitions[C]. IEEE International Conference on Image Processing, 2013: 1041-1045.
[2] Wan X, Gao Y Q, He X D. Three-dimensional flame temperature field reconstruction with multi-wavelength radiation computed tomography[J]. Acta Optica Sinica, 2003, 23(9): 1099-1104. 万雄, 高益庆, 何兴道. 多光谱辐射层析重建三维火焰温度场[J]. 光学学报, 2003, 23(9): 1099-1104.
[3] Brisley P M, Lu G, Yan Y, et al. Three-dimensional temperature measurement of combustion flames using a single monochromatic CCD camera[J]. IEEE Transactions on Instrumentation and Measurement, 2005, 54(4): 1417-1421.
[4] Ishino Y, Ohiwa N. Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame[J]. JSME International Journal Series B, 2005, 48(1): 34-40.
[5] Floyd J, Geipel P, Kempf A M. Computedtomography of chemiluminescence (CTC): Instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame[J]. Combustion and Flame, 2011, 158(2): 376-391.
[6] Li X S, Ma L. Volumetric imaging of turbulent reactive flows at kHz based on computed tomography[J]. Optics Express, 2014, 22(4): 4768-4778.
[7] Wang J, Song Y, Li Z H, et al. Multi-directional 3D flame chemiluminescence tomography based on lens imaging[J]. Optics Letters, 2015, 40(7): 1231-1234.
[8] Katz M B, Gordon R. Questions of uniqueness and resolution in reconstruction from projections[J]. Physics Today, 1979, 32(12): 52-56.
[9] Guédon J P, Normand N. The Mojette transform: the first ten years[C]. International Conference on Discrete Geometry for Computer Imagery, 2005: 79-91.
[10] Ji W P, Shen L S. Mojette transform and its applications to image processing[J]. Measurement & Control Technology, 2007, 26(3): 68-71. 计文平, 沈兰荪. Mojette变换及其应用[J]. 测控技术, 2007, 26(3): 68-71.
[11] Fayad H, Guédon J P, Svalbe I, et al. Applying Mojette discrete Radon transforms to classical tomographic data[J]. Proceedings of SPIE, 2008, 6913: 69132S.
[12] Hou W, Zhang C S. Parallel-beam CT reconstruction based on mojette transform and compressed sensing[J]. International Journal of Computer and Electrical Engineering, 2013, 5(1): 83-87.
[13] Li M J. The study on computed tomography image reconstruction algorithm based on compressed sensing theory[D]. Dalian: Dalian University of Technology, 2015. 李梦婕. 基于压缩感知理论的计算机层析图像重建算法[D]. 大连: 大连理工大学, 2015.
[14] Servières M, Normand N, Guédon J P, et al. The Mojette transform: discrete angles for tomography[J]. Electronic Notes in Discrete Mathematics, 2005, 20: 587-606.
[15] Song Y, Zhang B, He A Z. A novel iterative algorithm for moiré tomography[J]. Acta Optica Sinica, 2006, 26(3): 367-372. 宋旸, 张斌, 贺安之. 一种新的叠栅层析迭代算法[J]. 光学学报, 2006, 26(3): 367-372.
[16] Recur B, der Sarkissian H, Servières M, et al. Validation of Mojette reconstruction from Radon acquisitions[C]. IEEE International Conference on Image Processing, 2013: 1041-1045.