Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems

JW Stayman, JA Fessler - IEEE transactions on medical …, 2004 - ieeexplore.ieee.org
IEEE transactions on medical imaging, 2004ieeexplore.ieee.org
Imaging systems that form estimates using a statistical approach generally yield images with
nonuniform resolution properties. That is, the reconstructed images possess resolution
properties marked by space-variant and/or anisotropic responses. We have previously
developed a space-variant penalty for penalized-likelihood (PL) reconstruction that yields
nearly uniform resolution properties. We demonstrated how to calculate this penalty
efficiently and apply it to an idealized positron emission tomography (PET) system whose …
Imaging systems that form estimates using a statistical approach generally yield images with nonuniform resolution properties. That is, the reconstructed images possess resolution properties marked by space-variant and/or anisotropic responses. We have previously developed a space-variant penalty for penalized-likelihood (PL) reconstruction that yields nearly uniform resolution properties . We demonstrated how to calculate this penalty efficiently and apply it to an idealized positron emission tomography (PET) system whose geometric response is space-invariant. In this paper, we demonstrate the efficient calculation and application of this penalty to space-variant systems. (The method is most appropriate when the system matrix has been precalculated.) We apply the penalty to a large field of view PET system where crystal penetration effects make the geometric response space-variant, and to a two-dimensional single photon emission computed tomography system whose detector responses are modeled by a depth-dependent Gaussian with linearly varying full-width at half-maximum. We perform a simulation study comparing reconstructions using our proposed PL approach with other reconstruction methods and demonstrate the relative resolution uniformity, and discuss tradeoffs among estimators that yield nearly uniform resolution. We observe similar noise performance for the PL and post-smoothed maximum-likelihood (ML) approaches with carefully matched resolution, so choosing one estimator over another should be made on other factors like computational complexity and convergence rates of the iterative reconstruction. Additionally, because the postsmoothed ML and the proposed PL approach can outperform one another in terms of resolution uniformity depending on the desired reconstruction resolution, we present and discuss a hybrid approach adopting both a penalty and post-smoothing.
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