Hierarchical reconstruction using geometry and sinogram restoration

The authors describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates an object's mass, center of mass, and convex hull from the available projections, and uses this information, along with fundamental mathematical constraints, to estimate a full set of smoothed projections. The mass and center of mass estimates are made using a least squares estimator derived from the principles of consistency of the Radon transform. The convex hull estimate is produced by first estimating the positions of support lines of the object from each available projection and then estimating the overall convex hull using prior shape information. Estimating the position of two support lines from a single projection is accomplished using a generalized likelihood ratio technique for estimating jumps in linear systems. Results for simulated objects in a variety of measurement situations are shown, and several possible extensions to this work are discussed.

[1]  E. C. E. Owen,et al.  άπoτυμπανίζω, άπoτυμπανισμό (τυμπανισμό), τυμπανίζω, τύμπανoν (τύπανoν) , 1929 .

[2]  Shi-Kuo Chang,et al.  Two Algorithms for Multiple-View Binary Pattern Reconstruction , 1971, IEEE Trans. Syst. Man Cybern..

[3]  R. Gerchberg.  Super-resolution through Error Energy Reduction , 1974 .

[4]  A. Willsky,et al.  A generalized likelihood ratio approach to state estimation in linear systems subjects to abrupt changes , 1974, CDC 1974.

[5]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[6]  A. Willsky,et al.  A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems , 1976 .

[7]  E. Seppi,et al.  Stop-action cardiac computed tomography. , 1977, Radiology.

[8]  A. Willsky,et al.  A sequential method for spline approximation with variable knots. [recursive piecewise polynomial signal processing] , 1978 .

[9]  Tamon Inouye,et al.  Image Reconstruction with Limited Angle Projection Data , 1979, IEEE Transactions on Nuclear Science.

[10]  A. Louis,et al.  Picture reconstruction from projections in restricted range , 1980 .

[11]  M. E. Davison,et al.  Tomographic reconstruction with arbitrary directions , 1981 .

[12]  Douglas P. Boyd,et al.  Algorithms For Limited-Angle Computed Tomography , 1982, Other Conferences.

[13]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[14]  H Stark,et al.  Image restoration by convex projections in the presence of noise. , 1983, Applied optics.

[15]  Csaba K. Zoltani,et al.  Results of feasibility study on computer assisted tomography for ballistic applications. Technical report , 1983 .

[16]  Thomas S. Huang,et al.  Unified Hilbert space approach to iterative least-squares linear signal restoration , 1983 .

[17]  S. Deans.  The Radon Transform and Some of Its Applications , 1983 .

[18]  G. W. Wecksung,et al.  Bayesian approach to limited-angle reconstruction in computed tomography , 1983 .

[19]  M. Sezan,et al.  Tomographic Image Reconstruction from Incomplete View Data by Convex Projections and Direct Fourier Inversion , 1984, IEEE Transactions on Medical Imaging.

[20]  A. Willsky,et al.  Reconstruction from projections based on detection and estimation of objects--Parts I and II: Performance analysis and robustness analysis , 1984 .

[21]  S. B. Park,et al.  Iterative reconstruction-reprojection in projection space , 1985, Proceedings of the IEEE.

[22]  G. W. Wecksung,et al.  Local basis-function approach to computed tomography. , 1985, Applied optics.

[23]  S. B. Park,et al.  Projection Space Iteration Reconstruction-Reprojection , 1985, IEEE Transactions on Medical Imaging.

[24]  H. Trussell,et al.  Errors in Reprojection Methods in Computenzed Tomography , 1987, IEEE Transactions on Medical Imaging.

[25]  L. Shepp,et al.  Limited Angle Reconstruction in Tomography via Squashing , 1987, IEEE Transactions on Medical Imaging.

[26]  D. Wehner.  High Resolution Radar , 1987 .

[27]  M. Reha Civanlar,et al.  Error bounds for iterative reprojection methods in computerized tomography , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[28]  Mehrdad Soumekh,et al.  Binary image reconstruction from four projections , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[29]  Jerry L Prince.  Geometric model-based estimation from projections , 1988 .

[30]  M Ravichandran,et al.  Reconstruction of smooth distributions from a limited number of projections. , 1988, Applied optics.

[31]  Andrew Blake,et al.  Comparison of the Efficiency of Deterministic and Stochastic Algorithms for Visual Reconstruction , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  L. Younes.  Parametric Inference for imperfectly observed Gibbsian fields , 1989 .

[33]  Jerry L. Prince,et al.  Reconstructing Convex Sets from Support Line Measurements , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  G. Wahba.  Spline models for observational data , 1990 .

[35]  Jerry L Prince,et al.  A geometric projection-space reconstruction algorithm , 1990 .

[36]  P. Fishburn,et al.  Sets Uniquely Determined by Projections on Axes I , 1990 .

[37]  Jerry L Prince.  An Iterative Approach To Sinogram Restoration , 1990, [1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[38]  Jerry L. Prince,et al.  Constrained sinogram restoration for limited-angle tomography , 1990 .

[39]  Jerry L Prince,et al.  Consistency and convexity in object reconstruction from projections , 1990, 1990 IEEE International Conference on Systems Engineering.

[40]  Jerry L. Prince,et al.  Convex set reconstruction using prior shape information , 1991, CVGIP Graph. Model. Image Process..

[41]  Yoram Bresler,et al.  Image restoration by complexity regularization via dynamic programming , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[42]  Gabor T. Herman,et al.  Image Reconstruction From Projections , 1975, Real Time Imaging.