Journal of Biomedical Engineering Research (대한의용생체공학회:의공학회지)

The Korean Society of Medical and Biological Engineering (대한의용생체공학회)
권호 표지

A Spline-Regularized Sinogram Smoothing Method for Filtered Backprojection Tomographic Reconstruction

  • Lee, S.J. (Department of Electronic Engineering, Paichai University) ;
  • Kim, H.S. (Department of Electronic Engineering, Paichai University)
  • Published : 2001.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

Statistical reconstruction methods in the context of a Bayesian framework have played an important role in emission tomography since they allow to incorporate a priori information into the reconstruction algorithm. Given the ill-posed nature of tomographic inversion and the poor quality of projection data, the Bayesian approach uses regularizers to stabilize solutions by incorporating suitable prior models. In this work we show that, while the quantitative performance of the standard filtered backprojection (FBP) algorithm is not as good as that of Bayesian methods, the application of spline-regularized smoothing to the sinogram space can make the FBP algorithm improve its performance by inheriting the advantages of using the spline priors in Bayesian methods. We first show how to implement the spline-regularized smoothing filter by deriving mathematical relationship between the regularization and the lowpass filtering. We then compare quantitative performance of our new FBP algorithms using the quantitation of bias/variance and the total squared error (TSE) measured over noise trials. Our numerical results show that the second-order spline filter applied to FBP yields the best results in terms of TSE among the three different spline orders considered in our experiments.

Keywords

References

  1. IEEE Trans.Med.Imaging v.1 Maximum Likelihood Reconstruction for Emission Tomography Shepp;Y.Vardi
  2. IEEE Trans.Med.Imaging v.8 no.2 A Generalized EM Algorithm for 3-D Bayesian Reconstruction for Poisson Data Using Gibbs Priors T.Hebert;R.Leahy
  3. IEEE Trans.Med.Imaging v.MI-9 no.1 Bayesian Reconstructions from Emission Tomography Data using a Modified EM Algorithm P.J.Green
  4. Phys.Med.Biol. v.38 A Generalized Gibbs Prior for Maximum a Posteriori Reconstruction in SPECT D.S.Lalush;B.M.W.Tsui
  5. IEEE Trans.Med.Imaging v.14 no.4 Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Priors S.J.Lee;A.Rangarajan;G.Gindi
  6. IEEE Trans.Nuclear Science v.44 no.3 The Thin Plate as a Regularizer in Bayesian SPECT Reconstruction S.J.Lee;I.T.Hsias;G.R.Gindi
  7. IEEE Trans.Nuclear Science v.46 no.6 Validation of New Gibbs Priors for Bayesian Tomographic Recon struction Using Numerical Studies and Physically Acquired Data S.J.Lee;Y.Choi;G.Gindi
  8. Proc. SPIE: Image Reconstruction and Restoration Ⅱ v.3170 Quantitative Effects of Using Thin-Plate Priors in bayesian SPECT Reconstruction S.J.Lee;I.T.Hsiao;G.R.Gindi
  9. Image Reconstruction from Projections G.T.Herman
  10. Solution of Ⅲ-Posed Problems A.N.Tikhonov;V.Y.Arsenin
  11. IEEE Trans.patt.Anal.Mach.Intell. v.8 Regularization of Inverse Visual Problems involving Discontinuities D.Terzopoulos
  12. Computer Vision, Graphics, and Image Processing v.24 Multilevel Computational Processes for Visual Surface Reconstruction D.Terzopoulos
  13. Positron Emission Tomography and Autoradiography Principles of Single and Multiple Radionuclide Autoradiography J.L.Lear;M.E.Phelps(ed.);J.C.Mazziotta(ed.);H.R.Schelbert(ed.)