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改進的圖像重建迭代算法

張兆田,  張朋

張兆田, 張朋. 改進的圖像重建迭代算法[J]. 電子與信息學(xué)報, 2004, 26(10): 1626-1630.
引用本文: 張兆田, 張朋. 改進的圖像重建迭代算法[J]. 電子與信息學(xué)報, 2004, 26(10): 1626-1630.
Zhang Zhao-tian, Zhang Peng. An Algorithm for Improved Iterative Image Reconstruction[J]. Journal of Electronics & Information Technology, 2004, 26(10): 1626-1630.
Citation: Zhang Zhao-tian, Zhang Peng. An Algorithm for Improved Iterative Image Reconstruction[J]. Journal of Electronics & Information Technology, 2004, 26(10): 1626-1630.

改進的圖像重建迭代算法

An Algorithm for Improved Iterative Image Reconstruction

  • 摘要: 針對不完全數(shù)據(jù)圖像重建問題,該文從積分方程角度提出一種改進的圖像重建迭代算法(Im-proved Iterative Reprojection Reconstruction，IIRR)，并證明其在范數(shù)下收斂。該算法的圖像重建收斂速度和重建圖像誤差依賴于引入的參數(shù)因子、已知的投影數(shù)據(jù)與圖像的先驗信息。重建圖像可以表示為由已知投影數(shù)據(jù)所構(gòu)成圖像的級數(shù)形式。數(shù)值模擬結(jié)果表明，IIRR算法在不完全數(shù)據(jù)的情況下具有較好的圖像重建能力。
    Abstract: An Improved Iterative Reprojection Reconstruction (IIRR) from a view of in-tegral equation for incomplete image reconstruction is presented in this paper. IIRR is convergence under L~2 norm. The convergent velocity and the error of the reconstructed image depend on the relaxed parameter, the detected data and some prior information on image. The reconstructed image can be expressed in term of a series of image reconstructed by the detected data. Numerical simulation also shows that IIRR is effective to image reconstruction.
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  • Papoulis A. A new algorithm in spectra analysis and band-limited signal extrapolation. IEEE Trans. on Circuits Syst., 1975, CAS-22(9): 735-742.[2]Papoulis A. Signal Analysis. New York: McGraw-Hill, 1977: 205-215.[3]Gerchberg R W. Super-resolution through error energy reduction. Opt. Acta, 1974, 21(9): 709-720.[4]Gerchberg R W, Saxton W O. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik, 1972, 35(2): 237-246.[5]Chamzas C, Xu W Y. An improved version of Papoulis-Gerchberg algorithm on band-limited extrapolation. IEEE Trans. on Acoustics, Speech. Signal Processing, 1984, ASSP-32(2): 437-440.[6]Xu W Y, Chamzas C. On the extrapolation of band-limited functions with energy constraints[J].IEEE Trans. on Acoustic, Speech Signal Processing.1983, 31(5):1222-1234[7]Sanz J L, Huang T S. Discrete and continuous band-limited signal extrapolation. IEEE Trans.on Acoustic, Speech Signal Processing, 1983, ASSP-31(5): 1276-1285.[8]Sato T, Norton S J, et al.. Tomographic image reconstruction from limited projections using iterative revisions in image and transform space[J].Applied Optics.1981, 20(3):395-399[9]Peng H, Stark H. One-step image reconstruction from incomplete data in computer tomography.IEEE Trans. on Medical Imaging, 1989, MI-8(1): 16-31.[10]Virador P R G, et al.. 3D reconstruction in PET cameras with irregular sampling and depth of interaction[J].IEEE Trans. on Nuclear Science.2001, 48(4):1524-1529[11]張兆田,邱佩璋.一類廣義Radon變換的反演:迭代重建再投影的外插算法.CT理論與應(yīng)用研究,1993,2(3):20-23.
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出版歷程
  • 收稿日期:  2003-12-31
  • 修回日期:  2004-04-09
  • 刊出日期:  2004-10-19

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