Basic Principles of Tomographic Reconstruction

Synopsis: In this chapter the reader is introduced to the basic principles and tools of tomographic reconstruction. The chapter is divided into two sections: Part I provides the basics of computed tomography. Part II describes more advanced descriptions and methods.

[1]  Alexander Katsevich,et al.  Theoretically Exact Filtered Backprojection-Type Inversion Algorithm for Spiral CT , 2002, SIAM J. Appl. Math..

[2]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[3]  Dinggang Shen,et al.  3D conditional generative adversarial networks for high-quality PET image estimation at low dose , 2018, NeuroImage.

[4]  Mingshan Sun,et al.  Correction of photon attenuation and collimator response for a body-contouring SPECT/CT imaging system. , 2005, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[5]  Albert Macovski,et al.  A Maximum Likelihood Approach to Emission Image Reconstruction from Projections , 1976, IEEE Transactions on Nuclear Science.

[6]  T. Hebert,et al.  A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors. , 1989, IEEE transactions on medical imaging.

[7]  L. Lucy An iterative technique for the rectification of observed distributions , 1974 .

[8]  D S Lalush,et al.  A generalized Gibbs prior for maximum a posteriori reconstruction in SPECT. , 1993, Physics in medicine and biology.

[9]  Albert Macovski,et al.  A Maximum Likelihood Approach to Transmission Image Reconstruction from Projections , 1977, IEEE Transactions on Nuclear Science.

[10]  M. Goitein Three-dimensional density reconstruction from a series of two-dimensional projections , 1972 .

[11]  R. Bracewell Strip Integration in Radio Astronomy , 1956 .

[12]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

[13]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[14]  R. Q. Edwards,et al.  Image Separation Radioisotope Scanning , 1963 .

[15]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[16]  Alvaro R. De Pierro,et al.  A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography , 1996, IEEE Trans. Medical Imaging.

[17]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[18]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[19]  L. Feldkamp,et al.  Practical cone-beam algorithm , 1984 .

[20]  Bruce R. Rosen,et al.  Image reconstruction by domain-transform manifold learning , 2017, Nature.

[21]  K. Tanabe Projection method for solving a singular system of linear equations and its applications , 1971 .

[22]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[23]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.