Total-Variation Regularization in PositronEmission

We propose computational algorithms for incorporating total varia-tional (TV) regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects (e.g. tumors) that are distinguished from the background by sharp edges. We show that the standard EM algorithm can be modiied to incorporate the TV regularization, resulting in an algorithm that is robust independent of the amount of regularization.

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

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

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

[4]  K. Lange,et al.  EM reconstruction algorithms for emission and transmission tomography. , 1984, Journal of computer assisted tomography.

[5]  J. Mazziotta,et al.  Positron emission tomography and autoradiography , 1985 .

[6]  Michael I. Miller,et al.  The Use of Sieves to Stabilize Images Produced with the EM Algorithm for Emission Tomography , 1985, IEEE Transactions on Nuclear Science.

[7]  E. Veklerov,et al.  Stopping Rule for the MLE Algorithm Based on Statistical Hypothesis Testing , 1987, IEEE Transactions on Medical Imaging.

[8]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[9]  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.

[10]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  K. Lange.  Convergence of EM image reconstruction algorithms with Gibbs smoothing. , 1990, IEEE transactions on medical imaging.

[12]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[13]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[14]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[15]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[16]  Per Christian Hansen,et al.  Regularization methods for large-scale problems , 1993 .

[17]  Linda Kaufman,et al.  Maximum likelihood, least squares, and penalized least squares for PET , 1993, IEEE Trans. Medical Imaging.

[18]  Simon R. Cherry,et al.  Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images , 1994, IEEE Trans. Medical Imaging.

[19]  Luis Alvarez,et al.  Formalization and computational aspects of image analysis , 1994, Acta Numerica.

[20]  Curtis R. Vogel,et al.  Iterative Methods for Total Variation Denoising , 1996, SIAM J. Sci. Comput..

[21]  Chak-Kuen Wong,et al.  Total variation image restoration: numerical methods and extensions , 1997, Proceedings of International Conference on Image Processing.

[22]  Arnold Neumaier,et al.  Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization , 1998, SIAM Rev..

[23]  Tony F. Chan,et al.  Color TV: total variation methods for restoration of vector-valued images , 1998, IEEE Trans. Image Process..

[24]  Michel Barlaud,et al.  Variational approach for edge-preserving regularization using coupled PDEs , 1998, IEEE Trans. Image Process..