Abstract

In many applications of computed tomography, it may not be possible to acquire projection data at all angles, as required by the most commonly used algorithm of convolution backprojection. In such a limited-data situation, we face an ill-posed problem in attempting to reconstruct an image from an incomplete set of projections. Many techniques have been proposed to tackle this situation, employing diverse theories such as signal recovery, image restoration, constrained deconvolution, and constrained optimization, as well as novel schemes such as iterative object-dependent algorithms incorporating a priori knowledge and use of multispectral radiation. We present an overview of such techniques and offer a challenge to all readers to reconstruct images from a set of limited-view data provided here.

© 1985 Optical Society of America

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1985 (4)

P. J. Soble, R. M. Rangayyan, R. Gordon, “Quantitative and Qualitative Evaluation of Geometric Deconvolution of Artifacts in Limited-View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-32, 330 (1985).
[CrossRef]

A. P. Dhawan, R. M. Rangayyan, R. Gordon, “Image Restoration by Wiener Deconvolution in Limited-View Computed Tomography,” Appl. Opt. 24, this issue (Dec.1985).
[CrossRef] [PubMed]

R. Bamler, “Comments on Geometric Deconvolution: A Meta-Algorithm for Limited-View Computed Tomography,” IEEE Trans Biomed. Eng. BME-32, 241 (1985).
[CrossRef]

R. Gordon, A. P. Dhawan, R. M. Rangayyan, “Reply to ‘Comments on Geometric Deconvolution: A Meta-Algorithm for Limited-View Computed Tomography’” IEEE Trans. Biomed. Eng. BME-32, 242 (1985).
[CrossRef]

1984 (5)

A. P. Dhawan, R. Gordon, R. M. Rangayyan, “Nevoscopy: Three-dimensional Computed Tomography of Nevi and Melanomas in situ by Transillumination,” IEEE Trans. Med. Imaging MI-3, 54 (1984).
[CrossRef]

L. M. Cheng, A. S. Ho, R. E. Burge, “Use of a priori Knowledge in Image Reconstruction,” J. Opt. Soc. Am. A 1, 386 (1984).
[CrossRef]

M. I. Sezan, H. Stark, “Tomographic Image Reconstruction from Incomplete View Data by Convex Projections and Direct Fourier Inversion,” IEEE Trans. Med. Imaging MI-3, 91 (1984).
[CrossRef]

D. J. Rossi, A. S. Willsky, “Reconstruction from Projections Based on Detection and Estimation of Objects—Parts I and II: Performance Analysis and Robustness Analysis,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 886 (1984).
[CrossRef]

K. Ogawa, M. Nakajima, S. Yuta, “A reconstruction Algorithm from Truncated Projections,” IEEE Trans. Med. Imaging MI-3, 34 (1984).
[CrossRef]

1983 (20)

A. J. Devaney, “A Computer Simulation of Diffraction Tomography,” IEEE Trans. Biomed. Eng. BME-30, 377 (1983).
[CrossRef]

K. M. Hanson, G. W. Wecksung, “Bayesian Approach to Limited-Angle Reconstruction in Computed Tomography,” J. Opt. Soc. Am. 73, 1501 (1983).
[CrossRef]

H. Katsulai, N. Arimizu, “Reconstruction from Limited Angular Projection Data Using Constrained Optimization,” IEEE Trans. Nucl. Sci. NS-30, 1870 (1983).
[CrossRef]

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

C. L. Byrne, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, A. M. Darling, “Image Restoration and Resolution Enhancement,” J. Opt. Soc. Am. 73, 1481 (1983).
[CrossRef]

R. M. Rangayyan, R. Gordon, “Computed Tomography from Ordinary Radiographs for Teleradiology,” Med. Phys. 10, 687 (1983).
[CrossRef] [PubMed]

M. Defrise, C. de Mol, “A Regularized Iterative Algorithm for Limited-Angle Inverse Radon Transform,” Opt. Acta 30, 403 (1983).
[CrossRef]

A. Macovski, “Physical Problems of Computerized Tomography,” Proc. IEEE 71, 373 (1983).
[CrossRef]

A. K. Louis, F. Natterer, “Mathematical Problems of Computerized Tomography,” Proc. IEEE 71, 379 (1983).
[CrossRef]

M. Onoe, J. W. Tsao, H. Yamada, H. Nakamura, J. Kogure, H. Kawamura, M. Yoshimatsu, “Computed Tomography for Measuring Annual Rings of a Live Tree,” Proc. IEEE 71, 907 (1983).
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R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
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K. C. Tam, “Multispectral Limited-Angle Image Reconstruction,” IEEE Trans. Nucl. Sci. NS-30, 697 (1983).
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B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
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P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Reprojection Techniques,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
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A. M. Darling, T. J. Hall, M. A. Fiddy, “Stable, Noniterative Object Reconstruction from Incomplete Data Using a priori Knowledge,” J. Opt. Soc. Am. 73, 1466 (1983).
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J. M. Costa, A. N. Venetsanopoulos, M. Trefler, “Digital Tomographic Filtering of Radiographs,” IEEE Trans. Med. Imaging MI-2, 76 (1983).
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J. M. Costa, A. N. Venetsanopoulos, M. Trefler, “Design and Implementation of Digital Tomographic Filters,” IEEE Trans. Med. Imaging MI-2, 89 (1983).
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J. R. Spears, T. Sandor, R. Kruger, W. Hanlon, S. Paulin, G. Minerbo, “Computer Reconstruction of Luminal Cross Sectional Shape from Multiple Cineangiographic Views,” IEEE Trans. Med. Imaging MI-2, 49 (1983).
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J. J. Lefebvre, J. Marilleau, T. Rosseau, P. Tremelat, “Tomographic Reconstruction from a Limited Numbes of Projections,” Proc. Soc. Photo-Opt. Instrum. Eng. 312, 195 (1983).

R. A. Groenhuis, R. L. Webber, U. E. Ruttimann, “Computerized Tomosynthesis of Dental Tissues,” Oral Surg. Oral Med. Oral Pathol. 56, 206 (1983),
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1982 (30)

B. Macdonald, V. Perez-Mendez, “Contribution of Time-of-Flight Information to Limited Angle Positron Tomography,” IEEE Trans. Nucl. Sci. NS-29, 516 (1982).
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K. F. Koral, N. H. Clinthorne, W. L. Rogers, J. W. Keyes, “Feasibility of Sharpening Limited-Angle Tomography by Including an Orthogonal Set of Projections,” Nucl. Instrum. Methods 193, 223 (1982).
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K. M. Hanson, “CT Reconstruction from Limited Projection Angles,” Proc. Soc. Photo-Opt. Instrum. Eng. 347 (1982).

T. J. Hall, A. M. Darling, M. A. Fiddy, “Image Compression and Restoration Incorporating Prior Knowledge,” Opt. Lett. 7, 467 (1982).
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K. Kouris, H. Tuy, A. Lent, G. T. Herman, R. M. Lewitt, “Reconstructing from Sparsely Sampled Data by ART with Interpolated Rays,” IEEE Trans. Med. Imaging MI-1, 161 (1982).
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C. H. Slump, J. J. Gerbrands, “A Network Flow Approach to Reconstruction of the Left Ventricle from Two Projections,” Comput. Graphics Image Process. 18, 18 (1982).
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F. A. Grunbaum, “Limited Angle Reconstruction Problems in X-Ray and NMR Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 185 (1982).

G. A. Johnson, J. D. Godwin, E. K. Fram, “Gated Multiplanar Cardiac Computed Tomography,” Radiology 145, 195 (1982).
[PubMed]

Y. Koyanagi, I. Saito, Y. Hoshiko, “Image Reconstruction from Band-limited Data by Spectrum Extrapolation,” Trans. IECE Jpn. E65, 561 (1982).

T. Inouye, “Image Reconstruction with Limited View Angle Projections,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 165 (1982).

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
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W. H. Rowan, D. P. Boyd, J. L. Couch, D. Ortendahl, “Algorithms for Limited-Angle Computed Tomography,” Proc. Soc. Photo. Opt. Instrum. Eng. 372, 169 (1982).

S. K. Kenue, J. F. Greenleaf, “Limited Angle Multifrequency Diffraction Tomography,” IEEE Trans. Sonics Ultrason. SU-29, 213 (1982).
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N. Baba, K. Murata, “Image Reconstruction from Limited-Angle Projections,” Optik 60, 327 (1982).

K. C. Tam, “The Use of Multispectral Imaging in Limited-Angle Reconstruction,” IEEE Trans. Nucl. Sci. NS-29, 512 (1982).
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B. Cornuelle, “Acoustic Tomography,” IEEE Trans. Geosci. Remote Sensing GRS-20, 326 (1982).
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R. A. Robb, “X-ray Computed Tomography: An Engineering Synthesis of Multiscientific Principles,” CRC Crit. Rev. Biomed. Eng. 7, 264 (Mar.1982).

R. M. Rangayyan, R. Gordon, “Streak Preventive Image Reconstruction with ART and Adaptive Filtering,” IEEE Trans. Med. Imaging MI-1, 173 (1982).
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M. H. Reid, “Quantitative Stereology and Radiologic Image Analysis. Part I: Computerized Tomography and Ultra sound,” Med. Phys. 9, 346 (1982).
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A. Louis, “Nonuniqueness Problems in Computerized Tomography,” ZAMM- Angew. Anal. Math. Phys. 62, T290 (1982).

G. H. Weiss, A. J. Talbert, R. A. Brooks, “The Use of Phantom Views to Reduce CT Streaks due to Insufficient Angular Sampling,” Phys. Med. Biol. 27, 1151 (1982).
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B. P. Medoff, W. R. Brody, A. Macovski, “Image Reconstruction from Limited Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 188 (1982).

D. C. Youla, H. Webb, “Image Restoration by the Method of Convex Projections: Part 1—Theory,” IEEE Trans. Med. Imaging MI-1, 81 (1982).
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M. I. Sezan, H. Stark, “Image Restoration by the Method of Convex Projections: Part 2—Applications and Numerical Results,” IEEE Trans. Med. Imaging MI-1, 95 (1982).
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E. T. Jaynes, “On the Rationale of Maximum Entropy Methods,” Proc. IEEE 70, 939 (1982).
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R. Nityananda, R. Narayan, “Maximum Entropy Image Reconstruction—A Practical Noninformation-Theoretic Approach,” J. Astrophys. Astron. 3, 419 (1982).
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P. V. Sankar, O. Nalcioglu, J. Sklansky, “Undersampling Errors in Region-of-Interest Tomography,” IEEE Trans. Med. Imaging MI-1, 168 (1982).
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P. B. Heffernan, R. H. T. Bates, “Image Reconstruction from Projections. VI: Comparison of Interpolation Methods,” Optik 60, 129 (1982).

A. J. Devaney, “A Filtered Backpropagation Algorithm for Diffraction Tomography,” Ultrason. Imaging 4, 336 (1982).
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J. S. Choi, K. Ogawa, M. Nakajima, S. Yuta, “A Reconstruction Algorithm for Body Sections with Opaque Obstructions,” IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
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1981 (22)

M. H. Buonocore, W. R. Brody, A. Macovski, “A Natural Pixel Decomposition for Two-Dimensional Image Reconstruction,” IEEE Trans. Biomed. Eng. BME-28, 69 (1981).
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M. J. Lahart, “Estimation of Reconstructions in Computed Tomography,” J. Opt. Soc. Am. 71, 1155 (1981).
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M. H. Buonocore, W. R. Brody, A. Macovski, “Fast Minimum Variance Estimator for Limited Angle CT Image Reconstruction,” Med. Phys. 8, 695 (1981).
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R. J. Marks, M. J. Smith, “Closed-Form Object Restoration from Limited Spatial and Spectral Information,” Opt. Lett. 6, 522 (1981).
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H. Stark, D. Cahana, H. Webb, “Restoration of Arbitrary Finite-Energy Optical Objects from Limited Spatial and Spectral Information,” J. Opt. Soc. Am. 71, 635 (1981).
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R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained Iterative Restoration Algorithms,” Proc. IEEE 69, 432 (1981).
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M. Nassi, W. R. Brody, P. R. Cipriano, A. Macovski, “A Method for Stop-Action Imaging of the Heart Using Gated Computed Tomography,” IEEE Trans. Biomed. Eng. BME-28, 116 (1981).
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R. L. Morin, D. E. Raeside, “A Pattern Recognition Method for the Removal of Streaking Artifact in Computed Tomography,” Radiology 141, 229 (1981).
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A. K. Louis, “Ghosts in Tomography—The Null Space of the Radon Transform,” Math. Methods Appl. Sci. 3, 1 (1981).
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K. C. Tam, V. Perez-Mendez, “Limited Angle Three Dimensional Reconstructions Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
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K. C. Tam, V. Perez-Mendez, “Tomographical Imaging with Limited-Angle Input,” J. Opt. Soc. Am. 71, 582 (1981).
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K. C. Tam, V. Perez-Mendez, “Limits to Image Reconstruction from Restricted Angular Input,” IEEE Trans. Nucl. Sci. NS-28, 179 (1981).
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T. Sato, S. J. Norton, M. Linzer, O. Ikeda, M. Hirama, “Tomographic Image Reconstruction from Limited Projections Using Iterative Revisions in Image and Transform Spaces,” Appl. Opt. 20, 395 (1981).
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T. Sato, K. Saski, Y. Nakamura, M. Linzer, S. J. Norton, “Tomographic Image Reconstruction from Limited Projections Using Coherent Optical Feedback,” Appl. Opt. 20, 3073 (1981).
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A. Lent, H. Tuy, “An Iterative Method for Extrapolation of Band-limited Functions,” J. Math. Anal. Appl. 83, 554 (1981).
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H. Stark, J. W. Woods, I. Paul, R. Hingorani, “Direct Fourier Reconstruction in Computer Tomography,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 237 (1981).
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H. Tuy, “Reconstruction of.a Three-Dimensional Object from a Limited Range of Views,” J. Math. Anal. Appl. 80, 598 (1981).
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G. C. McKinnon, R. H. T. Bates, “Towards Imaging the Beating Heart Usefully with a Conventional CT Scanner,” IEEE Trans. Biomed. Eng. BME-28, 123 (1981).
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Y. S. Shim, Z. H. Cho, “SVD Pseudoinversion Image Reconstruction,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 904 (1981).
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B. Schorr, D. Townsend, “Filters for Three-Dimensional Limited-Angle Tomography,” Phys. Med. Biol. 26, 305 (1981).
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M. E. Davison, F. A. Grunbaum, “Tomographic Reconstruction with Arbitrary Directions,” Commun. Pure Appl. Math. 34, 77 (1981).
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C. H. Leung, H. C. Lee, “Effectiveness of Interpolation in the Time Domain for Computed Tomography of Moving Objects,” IEEE Trans. Biomed. Eng. BME-28, 582 (1981).

1980 (14)

J. C. Gore, S. Leeman, “The Reconstruction of Objects from Incomplete Projections,” Phys. Med. Biol. 25, 129 (1980).
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P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ec-omography: A New Radiographic Method for Reproducing a Selected Slice of Varying Thickness,” Acta Radiol. 21, 433 (1980).

J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer Generated Holograms,” Opt. Eng. 19, 297 (May/June1980).
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F. A. Grunbaum, “A Study of Fourier Space Methods for Limited Angle Image Reconstruction,” Numer. Function Anal. Optimiz. 2, 31 (1980).
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C. K. Rushforth, R. L. Frost, “Comparison of Some Algorithms for Reconstructing Space-Limited Images,” J. Opt. Soc. Am. 70, 1539 (1980).
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K. C. Tam, V. Perez-Mendez, B. Macdonald, “Limited Angle 3-D Reconstruction from Continuous and Pinhole Projections,” IEEE Trans. Nucl. Sci. NS-27, 445 (1980).
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A. J. Duerinckx, A. Macovski, “Information and Artifact in Computed Tomography Image Statistics,” Med. Phys. 7, 127 (1980).
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G. H. Glover, N. J. Pelc, “Nonlinear Partial Volume Artifacts in X-Ray Computed Tomography,” Med. Phys. 7, 238 (1980).
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P. S. Tofts, J. C. Gore, “Some Sources of Artifact in Computed Tomography,” Phys. Med. Biol. 25, 117 (1980).
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A. K. Louis, “Picture Reconstruction from Projections in Restricted Range,” Math. Methods Appl. Sci. 2, 209 (1980).
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D. Townsend, B. Schorr, A. Jeavons, “Three-Dimensional Image Reconstruction for a Positron Camera with Limited Angular Acceptance,” IEEE Trans. Nucl. Sci. NS-27, 463 (1980).
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T. S. Durrani, C. E. Goutis, “Optimisation Techniques for Digital Image Reconstruction from their Projections,” IEE Proc. 6, 161 (1980).

B. R. Frieden, “Image Restoration Using a Norm of Maximum Information,” Opt. Eng. 19, 290 (1980).
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M. C. Kemp, “Maximum Entropy Reconstruction in Emission Tomography,” Med. Radionuclide Imaging 1, 313 (1980).

1979 (25)

M. H. Buonocore, W. R. Brody, S. L. Wood, “Polar Pixel Kalman Filter for Limited Data Computed Tomography (CT) Image Reconstruction,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 109 (1979).

R. M. Lewitt, “Processing of Incomplete Measurement Data in Computed Tomography,” Med. Phys. 6, 412 (1979).
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O. Nalcioglu, P. V. Sankar, J. Sklansky, “Region of Interest X-Ray Tomography,” in Proc. Soc. Photo-Opt. Instrum. Eng. 206, 98 (1979).

O. Nalcioglu, Z. H. Cho, R. Y. Lou, “Limited Field of View Reconstruction in Computerized Tomography,” IEEE Trans. Nucl. Sci. NS-26, (1979).

A. Minami, T. Furukawa, “Three Dimensional Image Reconstruction from the Projections under Limited View Angle,” Trans. IECE Jpn. E62, 576 (1979).

G. Minerbo, “MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,” Comput. Graphics Image Process. 10, 48 (1979).
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J. Llacer, “Theory of Imaging with a Very Limited Number of Projections,” IEEE Trans. Nucl. Sci. NS-26, 596 (1979).
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R. F. Wagner, D. G. Brown, M. S. Pastel, “Application of Information Theory to the Assessment of Computed Tomography,” Med. Phys. 6, 83 (1979).
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A. Duerinckx, A. Macovski, “Information and Artifact in Second-Order Statistics from Computed Tomography (CT) Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 173, 250 (1979).

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “Aliasing: A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
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C. D. Stockham, “A Simulation Study of Aliasing in Computed Tomography,” Radiology 132, 721 (1979).
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A. C. Kak, “Computerized Tomography with X-ray, Emission, and Ultrasound Sources,” Proc. IEEE 67, 1245 (1979).
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J. G. Sanderson, “Reconstruction of Fuel Pin Bundles by a Maximum Entropy Method,” IEEE Trans. Nucl. Sci. NS-26, 2685 (1979).
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W. Munk, C. Wunsch, “Ocean Acoustic Tomography—A Scheme for Large Scale Monitoring,” Deep Sea Res. 26A, 123 (1979).

K. A. Dines, R. J. Lytle, “Computerized Geophysical Tomography,” Proc. IEEE, 67, 1065 (1979).
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C. R. Crawford, A. C. Kak, “Aliasing Artifacts in Computerized Tomography,” Appl. Opt. 18, 3704 (1979).
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K. C. Tam, V. Perez-Mendez, B. Macdonald, “3-D Object Reconstruction in Emission and Transmission Tomography with Limited Angular Input,” IEEE Trans. Nucl. Sci. NS-26, 2797 (1979).
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T. Inouye, “Image Reconstruction with Limited Angle Projection Data,” IEEE Trans. Nucl. Sci. NS-26, 2666 (1979).

M. Y. Chiu, H. H. Barrett, R. G. Simpson, C. Chou, J. W. Arendt, G. R. Gindi, “Three-Dimensional Radiographic Imaging with a Restricted View Angle,” J. Opt. Soc. Am. 69, 1323 (1979).
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R. W. Redington, W. H. Berninger, M. J. Lipton, B. Brundage, E. Carlsson, P. Doherty, “Cardiac Computed Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 67 (1979).

M. Nassi, W. R. Brody, P. Cipriano, P. Stonestrom, C. More-house, D. Moss, A. Macovski, “Application of a Reflection Technique for Improved Temporal Resolution with Dynamic ECG-Gated Computed Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 103 (1979).

Y. Tateno, T. Fujii, G. Uchiyama, Y. Masuda, “Methods for Cutting Time of ECG-Synchronized CT using Special X-ray Generator,” IEEE Trans. Nucl. Sci. NS-26, 2845 (1979).
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O. Nalcioglu, Z. H. Cho, R. Y. Lou, “Limited Field of View Reconstruction in Computerized Tomography,” IEEE Trans. Nucl. Sci. NS-26, 546 (1979).
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M. E. Davison, F. A. Grunbaum, “Convolution Algorithms for Arbitrary Projection Angles,” IEEE Trans. Nucl. Sci. NS-26, 2670 (1979).
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W. Wagner, “Reconstructions from Restricted Region Scan Data. New Means to Reduce Patient Dose,” IEEE Trans. Nucl. Sci. NS-26, 2866 (1979).
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1978 (13)

H. J. Scudder, “Introduction to Computer Aided Tomography,” Proc. IEEE 66, 628 (1978).
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L. A. Shepp, J. B. Kruskal, “Computerized Tomography: The New Medical X-ray Technology,” Am. Math. Mon. 85, 420 (1978).
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C. Hamaker, D. C. Solmon, “The Angles Between the Null Spaces of X-Rays,” J. Math. Anal. Appl. 62, 1 (1978).
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O. J. Tretiak, “Noise Limitations in X-Ray Computed Tomography,” J. Comput. Assist. Tomogr. 2, 477 (1978).
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R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assisted Tomogr. 2, 577 (1978).
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R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part III. Projection Completion Methods (Theory),” Optik 50, 189 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part I,” Optik 50, 19 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part II,” Optik 50, 85 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part IV. Projection Completion Methods (Computational Examples),” Optik 50, 269 (1978).

D. C. Youla, “Generalized Image Restoration by the Method of Alternating Orthogonal Projections,” IEEE Trans. Circuits Syst. CAS-25, 694 (1978).
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U. J. Schwarz, “Mathematical-Statistical Description of the Iterative Beam Removing Technique (Method CLEAN),” Astron. Astrophys. 65, 345 (1978).

B. K. P. Horn, “Density Reconstruction Using Arbitrary Ray Sampling Schemes,” Proc. IEEE 66, 551 (1978).
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B. R. Frieden, D. C. Wells, “Restoring with Maximum Entropy. III: Poisson Sources and Backgrounds,” J. Opt. Soc. Am. 68, 93 (1978).
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1977 (12)

A. J. Rockmore, A. Macovski, “A Maximum Likelihood Approach to Transmission Image Reconstruction from Projections,” IEEE Trans. Nucl. Sci. NS-24, 1929 (1977).
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S. J. Wernecke, L. R. D’Addario, “Maximum Entropy Image Reconstruction,” IEEE Trans. Comput. 26, 351 (1977).
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R. Kikuchi, B. H. Stoffer, “Maximum Entropy Image Restoration. I: The Entropy Expression,” J. Opt. Soc. Am. 67, 1656 (1977).
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R. Prost, R. Goutte, “Deconvolution when the Convolution Kernel has no Inverse,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 542 (1977).
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R. H. Huesman, “The Effects of a Finite Number of Projection Angles and Finite Lateral Sampling of Projections on the Propagation of Statistical Errors in Transverse Section Reconstruction,” Phys. Med. Biol. 22, 511 (1977).
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K. T. Smith, D. C. Solmon, S. L. Wagner, “Practical and Mathematical Aspects of the Problem of Reconstructing Objects from Radiographs,” Bull. Am. Math. Soc. 83, 1227 (1977).
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G. S. Harell, D. F. Guthaner, R. S. Brieman, C. C. Morehouse, E. J. Seppi, W. H. Marshall, L. Wexler, “Stop Action Cardiac Computed Tomography,” Radiology 123, 515 (May1977).
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G. V. Borgiotti, “Optimum Coherent Imaging of a Limited Field of View in the Presence of Angular and Aperture Noise,” J. Franklin Inst. 303, 155 (Feb.1977).
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G. Kowalski, “Fast 3-D Scanning Systems Using a Limited Tilting Angle,” Appl. Opt. 16, 1686 (1977).
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A. C. Kak, C. V. Jakowatz, N. A. Baily, R. A. Keller, “Computerized Tomography Using Video Recorded Fluoroscopic Images,” IEEE Trans. Biomed. Eng. BME-24, 157 (1977).
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N. A. Baily, “Computerized Tomography Using Video Techniques,” Opt. Eng. 16, 23 (1977).
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H. H. Barrett, W. Swindel, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
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1976 (3)

D. C. Solmon, “The X-Ray Transform,” J. Math. Anal. Appl. 56, 61 (1976).
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R. A. Brooks, G. di Chiro, “Principles of Computer Assisted Tomography (CAT) in Radiographic and Radioisotopic Imaging,” Phys. Med. Biol. 21, 689 (1976).
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R. A. Brooks, G. DiChiro, “Statistical Limitations in X-Ray Reconstructive Tomography,” Med. Phys. 3, 237 (1976).
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1975 (7)

B. F. Logan, “The Uncertainty Principle in Reconstructing Functions from Projections,” Duke Math. J. 42, 661 (1975).
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R. Gordon, G. T. Herman, S. A. Johnson, “Image Reconstruction from Projections,” Sci. Am. 233, 56 (Oct.1975).
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A. Papoulis, “A New Algorithm in Spectral Analysis and Band-limited Extrapolation,” IEEE Trans. Circuits Syst. CS-22, 735 (1975).
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S-K Chang, Y. R. Wang, “Three-Dimensional Object Reconstruction from Orthogonal Projections,” Pattern Recognition 7, 167 (1975).
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B.F. Logan, L. A. Shepp, “Optimal Reconstruction of a Function from its Projections,” Duke Math. J. 42, 645 (1975).
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Z. H. Cho, J. K. Chan, “A Comparative Study of 3-D Image Reconstruction Algorithms with Reference to Number of Projections and Noise Filtering,” IEEE Trans. Nucl. Sci. NS-22, 344 (1975).
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R. N. Bracewell, S. J. Wernecke, “Image Reconstruction ‘over a Finite Field of View,” J. Opt. Soc. Am. 65, 1342 (1975).
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1974 (7)

R. B. Guenther, C. W. Kerber, E. K. Killian, K. T. Smith, S. L. Wagner, “Reconstruction of Objects from Radiographs and Location of Brain Tumors,” Proc. Natl. Acad. Sci. USA 71, 4884 (1974).
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L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

R. Gordon, “A Tutorial on ART (Algebraic Reconstruction Techniques),” IEEE Trans. Nucl. Sci. NS-21, 78 (1974).

Z. H. Cho, “General Views on 3-D Image Reconstruction and Computerized Transverse Axial Tomography,” IEEE Trans. Nucl. Sci. 21, 44 (1974).

R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections: A Review of Algorithms,” Int. Rev. Cytol. 38, 111 (1974).
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R. M. Mersereau, A. V. Oppenheim, “Digital Reconstruction of Multidimensional Signals from Their Projections,” Proc. IEEE 62, 1319 (1974).
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R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
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1973 (5)

P. R. Smith, T. M. Peters, R. H. T. Bates, “Image Reconstruction from Finite Numbers of Projections,” J. Phys. A 6, 361 (1973).
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S-K Chang, C. K. Chow, “The Reconstruction of Three-Dimensional Objects from Two Orthogonal Projections and its Application to Cardiac Cineangiography,” IEEE Trans. Comput. C-22, 18 (1973).
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B. R. Altschuler, R. M. Perry, M. D. Altschuler, “Computerized Multiangular Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 40, 139 (1973).

J. Lau, “Remarks on Algorithm 445-Binary Pattern Reconstruction from Projections,” Commun. ACM 16, 186 (1973).

S.-K. Chang, “Algorithm 445-Binary Pattern Reconstruction from Projections,” Commun. ACM 16, 185 (1973).
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1972 (6)

D. G. Grant, “Tomosynthesis: A Three Dimensional Radiographic Imaging Technique,” IEEE Trans. Biomed. Eng. BME-19, 20 (1972).
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M. Goitein, “Three-Dimensional Density Reconstruction from a Series of Two Dimensional Projections,” Nucl. Instrum. Methods 101, 509 (1972).
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B. R. Frieden, J. J. Burke, “Restoring with Maximum Entropy. II: Superresolution of Photographs of Diffraction-Blurred Impulses,” J. Opt. Soc. Am. 62, 1202 (1972).
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B. R. Frieden, “Restoring with Maximum Likelihood and Maximum Entropy,” J. Opt. Soc. Am. 62, 511 (1972).
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A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature (London) 238, 435 (25Aug.1972).
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P. Gilbert, “Iterative Methods for the Three-Dimensional Reconstruction of an Object from Projections,” J. Theoret. Biol. 36, 105 (1972).
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1971 (6)

R. Gordon, G. T. Herman, “Reconstruction of Pictures from their Projections,” Commun. ACM 14, 759 (1971).
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J. Comput. Assisted Tomogr. (1)

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J. Franklin Inst. (1)

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J. Opt. Soc. Am. A (1)

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Math. Biosci. (1)

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Math. Methods Appl. Sci. (2)

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Med. Phys. (8)

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Med. Radionuclide Imaging (1)

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Nature (London) (1)

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Nucl. Instrum. Methods (2)

K. F. Koral, N. H. Clinthorne, W. L. Rogers, J. W. Keyes, “Feasibility of Sharpening Limited-Angle Tomography by Including an Orthogonal Set of Projections,” Nucl. Instrum. Methods 193, 223 (1982).
[CrossRef]

M. Goitein, “Three-Dimensional Density Reconstruction from a Series of Two Dimensional Projections,” Nucl. Instrum. Methods 101, 509 (1972).
[CrossRef]

Numer. Function Anal. Optimiz. (1)

F. A. Grunbaum, “A Study of Fourier Space Methods for Limited Angle Image Reconstruction,” Numer. Function Anal. Optimiz. 2, 31 (1980).
[CrossRef]

Opt. Acta (2)

M. Defrise, C. de Mol, “A Regularized Iterative Algorithm for Limited-Angle Inverse Radon Transform,” Opt. Acta 30, 403 (1983).
[CrossRef]

R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
[CrossRef]

Opt. Eng. (4)

K. C. Tam, V. Perez-Mendez, “Limited Angle Three Dimensional Reconstructions Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
[CrossRef]

J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer Generated Holograms,” Opt. Eng. 19, 297 (May/June1980).
[CrossRef]

N. A. Baily, “Computerized Tomography Using Video Techniques,” Opt. Eng. 16, 23 (1977).
[CrossRef]

B. R. Frieden, “Image Restoration Using a Norm of Maximum Information,” Opt. Eng. 19, 290 (1980).
[CrossRef]

Opt. Lett. (2)

Optik (6)

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part III. Projection Completion Methods (Theory),” Optik 50, 189 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part I,” Optik 50, 19 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part II,” Optik 50, 85 (1978).

R. M. Lewitt, R. H. T. Bates, “Image Reconstruction from Projections: Part IV. Projection Completion Methods (Computational Examples),” Optik 50, 269 (1978).

N. Baba, K. Murata, “Image Reconstruction from Limited-Angle Projections,” Optik 60, 327 (1982).

P. B. Heffernan, R. H. T. Bates, “Image Reconstruction from Projections. VI: Comparison of Interpolation Methods,” Optik 60, 129 (1982).

Oral Surg. Oral Med. Oral Pathol. (1)

R. A. Groenhuis, R. L. Webber, U. E. Ruttimann, “Computerized Tomosynthesis of Dental Tissues,” Oral Surg. Oral Med. Oral Pathol. 56, 206 (1983),
[CrossRef] [PubMed]

Pattern Recognition (1)

S-K Chang, Y. R. Wang, “Three-Dimensional Object Reconstruction from Orthogonal Projections,” Pattern Recognition 7, 167 (1975).
[CrossRef]

Phys. Med. Biol. (7)

E. Tanaka, A. T. Iinuma, “Correction Functions for Optimizing the Reconstructed Image in Transverse Section Scan,” Phys. Med. Biol. 20, 789.
[PubMed]

J. C. Gore, S. Leeman, “The Reconstruction of Objects from Incomplete Projections,” Phys. Med. Biol. 25, 129 (1980).
[CrossRef] [PubMed]

B. Schorr, D. Townsend, “Filters for Three-Dimensional Limited-Angle Tomography,” Phys. Med. Biol. 26, 305 (1981).
[CrossRef] [PubMed]

P. S. Tofts, J. C. Gore, “Some Sources of Artifact in Computed Tomography,” Phys. Med. Biol. 25, 117 (1980).
[CrossRef] [PubMed]

R. H. Huesman, “The Effects of a Finite Number of Projection Angles and Finite Lateral Sampling of Projections on the Propagation of Statistical Errors in Transverse Section Reconstruction,” Phys. Med. Biol. 22, 511 (1977).
[CrossRef] [PubMed]

R. A. Brooks, G. di Chiro, “Principles of Computer Assisted Tomography (CAT) in Radiographic and Radioisotopic Imaging,” Phys. Med. Biol. 21, 689 (1976).
[CrossRef] [PubMed]

G. H. Weiss, A. J. Talbert, R. A. Brooks, “The Use of Phantom Views to Reduce CT Streaks due to Insufficient Angular Sampling,” Phys. Med. Biol. 27, 1151 (1982).
[CrossRef] [PubMed]

Proc. IEEE (11)

R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained Iterative Restoration Algorithms,” Proc. IEEE 69, 432 (1981).
[CrossRef]

R. M. Mersereau, A. V. Oppenheim, “Digital Reconstruction of Multidimensional Signals from Their Projections,” Proc. IEEE 62, 1319 (1974).
[CrossRef]

M. Onoe, J. W. Tsao, H. Yamada, H. Nakamura, J. Kogure, H. Kawamura, M. Yoshimatsu, “Computed Tomography for Measuring Annual Rings of a Live Tree,” Proc. IEEE 71, 907 (1983).
[CrossRef]

A. C. Kak, “Computerized Tomography with X-ray, Emission, and Ultrasound Sources,” Proc. IEEE 67, 1245 (1979).
[CrossRef]

H. J. Scudder, “Introduction to Computer Aided Tomography,” Proc. IEEE 66, 628 (1978).
[CrossRef]

A. Macovski, “Physical Problems of Computerized Tomography,” Proc. IEEE 71, 373 (1983).
[CrossRef]

A. K. Louis, F. Natterer, “Mathematical Problems of Computerized Tomography,” Proc. IEEE 71, 379 (1983).
[CrossRef]

K. A. Dines, R. J. Lytle, “Computerized Geophysical Tomography,” Proc. IEEE, 67, 1065 (1979).
[CrossRef]

H. H. Barrett, W. Swindel, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
[CrossRef]

E. T. Jaynes, “On the Rationale of Maximum Entropy Methods,” Proc. IEEE 70, 939 (1982).
[CrossRef]

B. K. P. Horn, “Density Reconstruction Using Arbitrary Ray Sampling Schemes,” Proc. IEEE 66, 551 (1978).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

R. B. Guenther, C. W. Kerber, E. K. Killian, K. T. Smith, S. L. Wagner, “Reconstruction of Objects from Radiographs and Location of Brain Tumors,” Proc. Natl. Acad. Sci. USA 71, 4884 (1974).
[CrossRef] [PubMed]

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (11)

M. Nassi, W. R. Brody, P. Cipriano, P. Stonestrom, C. More-house, D. Moss, A. Macovski, “Application of a Reflection Technique for Improved Temporal Resolution with Dynamic ECG-Gated Computed Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 103 (1979).

B. P. Medoff, W. R. Brody, A. Macovski, “Image Reconstruction from Limited Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 188 (1982).

R. W. Redington, W. H. Berninger, M. J. Lipton, B. Brundage, E. Carlsson, P. Doherty, “Cardiac Computed Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 67 (1979).

T. Inouye, “Image Reconstruction with Limited View Angle Projections,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 165 (1982).

A. Duerinckx, A. Macovski, “Information and Artifact in Second-Order Statistics from Computed Tomography (CT) Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 173, 250 (1979).

B. R. Altschuler, R. M. Perry, M. D. Altschuler, “Computerized Multiangular Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 40, 139 (1973).

J. J. Lefebvre, J. Marilleau, T. Rosseau, P. Tremelat, “Tomographic Reconstruction from a Limited Numbes of Projections,” Proc. Soc. Photo-Opt. Instrum. Eng. 312, 195 (1983).

K. M. Hanson, “CT Reconstruction from Limited Projection Angles,” Proc. Soc. Photo-Opt. Instrum. Eng. 347 (1982).

F. A. Grunbaum, “Limited Angle Reconstruction Problems in X-Ray and NMR Tomography,” Proc. Soc. Photo-Opt. Instrum. Eng. 372, 185 (1982).

O. Nalcioglu, P. V. Sankar, J. Sklansky, “Region of Interest X-Ray Tomography,” in Proc. Soc. Photo-Opt. Instrum. Eng. 206, 98 (1979).

M. H. Buonocore, W. R. Brody, S. L. Wood, “Polar Pixel Kalman Filter for Limited Data Computed Tomography (CT) Image Reconstruction,” Proc. Soc. Photo-Opt. Instrum. Eng. 206, 109 (1979).

Proc. Soc. Photo. Opt. Instrum. Eng. (1)

W. H. Rowan, D. P. Boyd, J. L. Couch, D. Ortendahl, “Algorithms for Limited-Angle Computed Tomography,” Proc. Soc. Photo. Opt. Instrum. Eng. 372, 169 (1982).

Radiology (5)

R. L. Morin, D. E. Raeside, “A Pattern Recognition Method for the Removal of Streaking Artifact in Computed Tomography,” Radiology 141, 229 (1981).
[PubMed]

C. D. Stockham, “A Simulation Study of Aliasing in Computed Tomography,” Radiology 132, 721 (1979).
[PubMed]

G. A. Johnson, J. D. Godwin, E. K. Fram, “Gated Multiplanar Cardiac Computed Tomography,” Radiology 145, 195 (1982).
[PubMed]

G. S. Harell, D. F. Guthaner, R. S. Brieman, C. C. Morehouse, E. J. Seppi, W. H. Marshall, L. Wexler, “Stop Action Cardiac Computed Tomography,” Radiology 123, 515 (May1977).
[PubMed]

E. R. Miller, E. W. McCurry, B. Hruska, “An Infinite Number of Laminagrams from a Finite Number of Radiographs,” Radiology 98, 249 (1971).
[PubMed]

Sci. Am. (1)

R. Gordon, G. T. Herman, S. A. Johnson, “Image Reconstruction from Projections,” Sci. Am. 233, 56 (Oct.1975).
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SIAM J. Appl. Math. Anal. (1)

M. E. Davison, “The Ill-Conditioned Nature of the Limited Angle Tomography Problem,” SIAM J. Appl. Math. Anal. 428 (1983–1984).

Trans. IECE Jpn. (2)

Y. Koyanagi, I. Saito, Y. Hoshiko, “Image Reconstruction from Band-limited Data by Spectrum Extrapolation,” Trans. IECE Jpn. E65, 561 (1982).

A. Minami, T. Furukawa, “Three Dimensional Image Reconstruction from the Projections under Limited View Angle,” Trans. IECE Jpn. E62, 576 (1979).

Ultrason. Imaging (1)

A. J. Devaney, “A Filtered Backpropagation Algorithm for Diffraction Tomography,” Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

ZAMM- Angew. Anal. Math. Phys. (1)

A. Louis, “Nonuniqueness Problems in Computerized Tomography,” ZAMM- Angew. Anal. Math. Phys. 62, T290 (1982).

Other (71)

M. B. Katz, Questions of Uniqueness and Resolution in Reconstruction from Projections, in series Lecture Notes in Bio-mathematics, S. Levin, Ed. (Springer-Verlag, Berlin, 1979).

L. A. Shepp, J. A. Stein, “Simulated Reconstruction Artifacts in Computerized X-Ray Tomography,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. M. Ter-Pogossian et al., Ed. (University Park Press, Baltimore, 1977), pp. 33–48.

M. Ein-Gal, D. Rosenfeld, A. Macovski, “The Consistency of the Shadow: An Approach to Preprocessing in Computerized Tomography,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper WB5.

L. Garnero, J. Brunol, “Tomographic Imaging with Limited View Angle Using an Expansion on a Set of Eigenfunctions Adapted to Space-Limited Objects,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA4.

P. R. Smith, T. M. Peters, R. M. Lewitt, R. H. T. Bates, “Aspects of Image Reconstruction by Fourier Methods,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper TLA4.

N. H. Farhat, “Inverse Scattering Reconstructions from Incomplete Fourier Space Data,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA9.

G. T. Herman, Ed., Image Reconstruction From Projections: Implementation and Applications (Springer-Verlag, Berlin, 1979).
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G. T. Herman, Image Reconstruction From Projections: The Fundamentals Of Computed Tomography (Academic, New York, 1980).

A. Rosenfeld, A. C. Kak, “Reconstruction,” in Digital Picture Processing (Academic, New York, 1982), Chap. 8, pp. 353–430.

H. H. Barrett, W. Swindel, Radiological Imaging, Vols. 1 and 2 (Academic, New York, 1982).

J. Raviv, J. F. Greenleaf, G. T. Herman, Eds., Computer Aided Tomography and Ultrasonics in Medicine (North-Holland, Amsterdam, 1979).

A. Macovski, Medical Imaging Systems (Prentice-Hall, Englewood Cliffs, N.J., 1983).

D. A. Terry, J. N. Albright, “Numerical Simulations in Limited-Aperture Tomography with Application to Crosswell Acoustics,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of America, Washington, D.C., 1984), paper TuA2.

J. N. Albright, D. A. Terry, “Crosswell Acoustic Imaging Project June 1984 Review,” LA-UR-84-1928, Los Alamos Scientific Laboratory (1984).

S. Persson, E. Ostman, “Use of Computed Tomography in Non-destructive Testing of Polymeric Materials,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of America, Washington, D.C., 1984), paper MB5.

W. A. Ellingson, M. Vannier, “Application of Tomographic Imaging to Structural Ceramics: Green-state Monolithics and Ceramic-Ceramic Composites,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of America, Washington, D.C., 1984), paper MB6.

R. Gordon, H. V. B. Hirsch, “Vision Begins with Reconstructions of the Retinal Image: How the Brain Sees and Stores Pictures,” in Im Gegenstrom-Fuer Helmut Hirsch zum Siebzigsten (Peter Hammer Verlag, Wuppertal, 1976), pp. 201–214.

D. L. Snyder, J. R. Cox, “An Overview of Reconstructive Tomography and Limitations Imposed by a Finite Number of Projections,” in Reconstructive Tomography in Diagnostic Radiology and Nuclear Medicine, M. M. Ter-Pogossian et al., Eds. (University Park Press, Baltimore, 1977), pp. 3–32.

R. Gordon, “Artifacts in Reconstructions made from a Few Projections,” in Proceedings, First International Joint Conference on Pattern Recognition (IEEE Computer Society, Washington, D.C., 1973), pp. 275–285.

H. Stark, I. M. Sezan, “Image Restoration by the Method of Projections onto Convex Sets,” in Technical Digest, Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper WA8.

A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).

B. R. Frieden, “Image Enhancement and Restoration,” in Topics in Applied Physics, Vol. 6: Picture Processing and Digital Filters, T. S. Huang, Ed. (Springer-Verlag, New York, 1975).

R. Gordon, R. M. Rangayyan (M. R. Rangaraj), “Experiments on Streak Prevention in Image Reconstruction from a Few Views,” in Proceedings, Fourth Biennial Conference Canadian Society for Computational Studies of Intelligence (Saskatoon, May1982), pp. 41–47.

O. J. Tretiak, “The Point-Spread Function for the Convolutional Algorithm, Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper ThA5.

B. E. Oppenheim, “Reconstruction Tomography from Incomplete Projections,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. M. Ter-Pogossian et al., Eds. (University Park Press, Baltimore, 1977), pp. 155–183.

R. M. Rangayyan, R. Gordon, “Geometric Deconvolution of Artifacts in Limited View Computed Tomography,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA2.

A. P. Dhawan, R. Gordon, R. M. Rangayyan, “Computed Tomography by Translumination to Detect Early Melanoma,” in Proceedings, Frontiers of Engineering and Computing in Health Care (IEEE, Los Angeles, 1984), pp. 518–522.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, New York, 1979).

A. P. Dhawan, R. M. Rangayyan, R. Gordon, “Wiener Filtering for Deconvolution of Geometric Artifacts in Limited-View Computed Tomography,” in Proceedings, Medical Images and Icons Conference (IEEE Computer Society, Arlington, 1984), pp. 168–172.
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A. P. Dhawan, R. M. Rangayyan, R. Gordon, “Image Restoration by Two-Dimensional Deconvolution in Limited-View Reconstruction,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of American, Washington, D.C., 1984), paper TuA5.

P. B. Heffernan, R. A. Robb, “Towards Improved Reconstruction of the Heart from Small Numbers of Projections,” in Computers in Cardiology (IEEE Computer Society, Silver Spring, Md.) 1982, pp. 149–152.

H. Ogawa, “Image Reconstruction from Incomplete Projections,” in Proceedings, First International Symposium on Medical Imaging Image Interpretation ISMII ’82 (IEEE, Berlin, 1982), pp. 534–539.
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S. Renjen, T. S. Huang, “Experimental Results on the Missing Cone Problem in Computer Aided Tomography,” in Proceedings, Fifth Annual Symposium on Computer Applications in Medical Care, H. G. Heffernan, Ed. (IEEE Computer Society, Washington, D.C., 1981), pp. 566–570.

A. J. Devaney, “Coherent Optical Tomography,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of America, Washington, D.C., 1984), paper TuD3.

G. W. Wecksung, K. M. Hanson, “Some Results on the Use of Local Basis Functions for Reconstruction Representation in Computed Tomography,” in Technical Digest, Topical Meeting on Industrial Applications of Computed Tomography and NMR Imaging (Optical Society of America, Washington, D.C., 1984), paper TuC5.

Th. Hinderling, P. Ruegsegger, M. Anliker, “CT Reconstruction from Hollow Projections: An Application to in vivo Evaluation of Artificial Hip Joints,” in Third International Conference on Bone Measurements, New Orleans (1976).

D. G. W. Onnasch, W. Schmitz, P. H. Heintzen, “Problems of the Binary Reconstruction of the Left and Right Ventricles from Biplane Angiocardiograms,” in Digital Imaging in Cardiovascular Radiology: International Symposium Kiel, R. Brennecke, G. Thieme, Eds. (Springer-Verlag, Stuttgart, 1983), pp. 141–151.

J. H. C. Reiber, J. J. Gerbrands, G. J. Troost, C. J. Kooijman, C. H. Slump, “3-D Reconstruction of Coronal Arterial Segments for Two Projections,” Digital Imaging in Cardiovascular Radiology: International Symposium Kiel, R. Brennecke, G. Thieme, Eds. (Springer-Verlag, Stuttgart, 1983), pp. 151–163.

G. T. Herman, “Reconstruction of Binary Patterns from a Few Projections,” in International Computing Symposium (1973), A. Gunther et al., Eds. (North-Holland, New York, 1974), pp. 371–379.

Y. Bresler, A. Macovski, “A Hierarchical Bayesian Approach to Reconstruction from Projections of a Multiple Object 3-D Scene,” in Proceedings, Seventh International Conference, Pattern Recognition (IEEE, New York, 1984), pp. 455–457.

Y. Bresler, A. Macovski, “Estimation of 3-D Shape of Blood Vessels from X-Ray Images,” in Proceedings, International Symposium on Medical Images and Icons (IEEE Computer Society, New York, 1984), pp. 251–258.
[CrossRef]

Y. Bresler, A. Macovski, “3-D Reconstruction from Projections Based on Dynamic Object Models,” in Proceedings International Conference on Acoustics, Speech, and Signal Processing (IEEE, New York, 1984).

M. J. Lahart, “Linear Estimation with a Size Constraint,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA5.

B. E. Oppenheim, “Three Dimensional Reconstruction from Incomplete Projections,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper WA1.

R. H. T. Bates, R. M. Lewitt, T. M. Peters, P. R. Smith, “Image Reconstruction from Incomplete Projections,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper WA2.

S. C. Huang, M. E. Phelps, E. J. Hoffman, “Effect of Out-of-Field Objects in Transaxial Reconstruction Tomography,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. M. Ter-Pogossian et al., Eds. (University Park Press, Baltimore, 1977), pp. 185–198.

A. Lent, “A Convergent Algorithm for Maximum Entropy Image Reconstruction with a Medical X-Ray Application,” in Image Analysis and Evaluation, R. Shaw, Ed. (Society of Photographic Scientists and Engineers, Washington, D.C., 1977), pp. 249–257.

T. Elfring, “A Method for Computing the Maximum Entropy Solution of a Linear System,” LiTh-MAT-R-1978-4, Department of Mathematics, Linkoping U., Linkoping, Sweden (1978).

J. P. Burg, “Maximum Entropy Spectral Analysis,” in Proceedings, Thirty-seventh Meeting of the Society of Exploration Geophysicists, Oklahoma City (1967).

S. F. Gull, G. J. Daniell, “The Maximum Entropy Method,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (D. Reidel, Hingham, Mass., 1979), pp. 219–225.
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T. J. Cornwell, “The Use of Bayesian Statistics in Image Estimation from Interferometer Data,” Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (D. Reidel, Hingham, Mass., 1979), pp. 227–234.
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K. M. Hanson, G. W. Wecksung, “Bayesian Approach to Limited-Angle CT Reconstruction,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA6.

D. J. Rossi, A. S. Willsky, “Localization from Projections Based on Detection and Estimation of Objects,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA3.

H. Hurwitz, J. E. Rumbaugh, “Comparison of Point Response Function and Bayesian Criteria in Image Reconstruction,” 76CRD207, General Electric Corporate Research and Development, Schenectady, N.Y. (1977).

A. J. Rockmore, A. Macovski, “A Maximum Likelihood Approach to Image Reconstruction,” in Proceedings, Joint Automatic Control Conference, San Francisco (1977), pp. 782–786.

S. L. Wood, M. Morf, A. Macovski, “Stochastic Methods Applied to Medical Image Reconstruction,” in Proceedings, IEEE Conference on Decision and Control (IEEE, New York, 1977), pp. 35–41.

S. L. Wood, A. Macovski, M. Morf, “Reconstructions with Limited Data Using Estimation Theory,” in Computer Aided Tomography and Ultrasonics in Medicine, G. T. Herman, Ed. (North-Holland, Amsterdam, 1979), pp. 219–233.

S. Sibisi, “Two-Dimensional Reconstructions from One-Dimensional Data by Maximum Entropy,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA11

L. R. D’Addario, “Maximum a Posteriori Probability and Maximum Entropy Reconstruction,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper WA5.

S. J. Wernecke, “Maximum Entropy Image Reconstruction,” in Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences, R. Gordon, Ed. (Optical Society of America, Washington, D.C., 1975), paper WA6.

U. E. Ruttimann, R. A. J. Groenhuis, R. L. Webber, “Computer Tomosynthesis: A Versatile Three-Dimensional Imaging Technique,” in Proceeding, Seventh Annual Symposium on Computer Applications in Medical Care (IEEE Computer Society, Silver Spring, Md., 1983), pp. 7833–786.

A. M. Darling, T. J. Hall, M. Fiddy, “Stable, Noniterative, Object Reconstruction from Incomplete Data Using Prior Knowledge,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper WA9.

H. K. Tuy, “An Algorithm for Incomplete Range of Views Reconstruction,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA1.

K. M. Hanson, “Limited Angle CT Reconstruction Using a priori Information,” in Proceedings First International Symposium on Medical Imaging Image Interpretation ISMII ’82 (IEEENew York, 1982), pp. 527–533.
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B. P. Medoff, W. R. Brody, A. Macovski, “The Use of a priori Information in Image Reconstruction from Limited Data,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA7.

R. G. Paxman, G. R. Gindi, H. H. Barrett, “Incorporation of Prior Constraints in Tomographic Reconstruction from Coded Images,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper FA8.

J. Gassmann, “Optimal Iterative Image Reconstruction with Incomplete and Approximate Data,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints, (Optical Society of America, Washington, D.C., 1983), paper WA11.

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of Objects from Coded Images by Simulated Annealing,” in Technical Digest, Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), paper WA13.

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Tables (1)

Tables Icon

Table I Projection Data

Metrics