  In a low-statistics PET imaging context, the positive bias in regions of low
activity is a burning issue. To overcome this problem, algorithms without the
built-in non-negativity constraint may be used. They allow negative voxels in
the image to reduce, or even to cancel the bias. However, such algorithms
increase the variance and are difficult to interpret, since negative
radioactive concentrations have no physical meaning. Here, we propose a
post-processing strategy to remove negative intensities while preserving the
local mean activities. Our idea is to transfer the negative intensities to
neighboring voxels, so that the mean of the image is preserved. The proposed
post-processing algorithm solves a linear programming problem with a specific
symmetric structure, and the solution can be computed in a very efficient way.
Acquired data from an yttrium-90 phantom show that on images produced by a
non-constrained algorithm, a much lower variance in the cold area is obtained
after the post-processing step.
