Nonlocal Prior Bayesian Tomographic Reconstruction
Journal of Mathematical Imaging and Vision
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Iterative methods for tomographic image reconstruction often converge slowly. Preconditioning methods can often accelerate gradient-based iterations. Previous preconditioning methods for PET reconstruction have used either diagonal or Fourier-based preconditioners. Fourier-based preconditioners are well suited to problems with near-circulant Hessian matrices. However, due to the nonuniform Poisson noise variance in PET, the circulant approximation to the Hessian is suboptimal. This paper shows that a particular combined diagonal/Fourier preconditioner yields a more accurate approximation to the Hessian and gives significantly faster convergence rates than does either preconditioner used alone.