We present an adaptive method of selecting the center weight in the weighted-median prior for penalized-likelihood (PL)
transmission tomography reconstruction. While the well-known median filter, which is closely related to the median
prior, preserves edges, it is known to have an unfortunate effect of removing fine details because it tends to eliminate
any structure that occupies less than half of the window elements. On the other hand, center-weighted median filters can
preserve fine details by using relatively large center weights. But the large center weights can degrade monotonic
regions due to insufficient noise suppression. In this work, to adaptively select the center weight, we first calculate pixelwise
standard deviation over 3×3 neighbors of each pixel at every PL iteration and measure its cumulative histogram,
which is a monotonically non-decreasing 1-D function. We then normalize the resulting function to maintain its range
over [1,9]. In this case the domain of the normalized function represents the standard deviation at each pixel, and the
range can be used for the center weight of a 3×3 median window. We implemented the median prior within the PL
framework and used an alternating joint minimization algorithm based on a separable paraboloidal surrogates algorithm.
The experimental results demonstrate that our proposed method not only compromises the two extreme cases (the largest
and smallest center weights) yielding a good reconstruction over the entire image in terms of the percentage error, but
also outperforms the standard method in terms of the contrast recovery coefficient measured in several regions of interest.