Regularizing images in emission tomography via an extension ofGoodapos;s roughness penalty
Snyder, D.L.; Lanterman, A.D.; Miller, M.I.
Nuclear Science Symposium and Medical Imaging Conference, 1992., Conference Record of the 1992 IEEE
Volume , Issue , 25-31 Oct 1992 Page(s):1223 vol.2 -
Digital Object Identifier 10.1109/NSSMIC.1992.301484
Summary:Summary form only given, as follows. Good's roughness penalty has
been used previously for regularizing maximum likelihood estimates of
radionuclide distributions by constraining the energy in the first
derivative of the square root of the estimate, where the square root is
used to enforce the nonnegativity of the estimate. The authors
investigate the implications of constraining the energy in the
nth derivative of the function. The extended penalty is
equivalent to a Markov random field or Gibbs' prior in which the
neighborhood of any pixel includes the 2n(n+1) closest
pixels that surround it. Although the reconstructions are nonlinear, it
is shown how nth order Butterworth filters arise as natural
smoothing kernels. A comparison has been made between estimates in SPECT
(single photon emission computed tomography) produced by maximum
likelihood penalized with the extended nth-order Good's
roughness, for orders one to five, and those produced by the method of
filtered backprojection with Butterworth smoothing for a filter
corresponding order
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