Regularizing images in emission tomography via an extension of Good´s roughness penalty

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