Bilateral filtration has proven an effective tool for denoising CT data. The classic filter uses Gaussian domain and range
weighting functions in 2D. More recently, other distributions have yielded more accurate results in specific applications,
and the bilateral filtration framework has been extended to higher dimensions. In this study, brute-force optimization is
employed to evaluate the use of several alternative distributions for both domain and range weighting: Andrew's Sine
Wave, El Fallah Ford, Gaussian, Flat, Lorentzian, Huber's Minimax, Tukey's Bi-weight, and Cosine. Two variations on
the classic bilateral filter, which use median filtration to reduce bias in range weights, are also investigated: median-centric
and hybrid bilateral filtration. Using the 4D MOBY mouse phantom reconstructed with noise (stdev. ~ 65 HU),
hybrid bilateral filtration, a combination of the classic and median-centric filters, with Flat domain and range weighting
is shown to provide optimal denoising results (PSNRs: 31.69, classic; 31.58 median-centric; 32.25, hybrid). To validate
these phantom studies, the optimal filters are also applied to in vivo, 4D cardiac micro-CT data acquired in the mouse. In
a constant region of the left ventricle, hybrid bilateral filtration with Flat domain and range weighting is shown to
provide optimal smoothing (stdev: original, 72.2 HU; classic, 20.3 HU; median-centric, 24.1 HU; hybrid, 15.9 HU).
While the optimal results were obtained using 4D filtration, the 3D hybrid filter is ultimately recommended for denoising
4D cardiac micro-CT data, because it is more computationally tractable and less prone to artifacts (MOBY PSNR: 32.05;
left ventricle stdev: 20.5 HU).