  The speckle statistics of optical coherence tomography images of biological
tissue have been studied using several historical probability density
functions. A recent hypothesis implies that underlying power-law distributions
in the medium structure, such as the fractal branching vasculature, will
contribute to power-law probability distributions of speckle statistics.
Specifically, these are the Burr type XII distribution for speckle amplitude,
the Lomax distribution for intensity, and the generalized logistic distribution
for log amplitude. In this study, these three distributions are fitted to
histogram data from nine optical coherence tomography scans of various
biological tissues and samples. The distributions are also compared with
conventional distributions such as the Rayleigh, K, and gamma distributions.
The results indicate that these newer distributions based on power laws are, in
general, more appropriate models and support the plausibility of their use for
characterizing biological tissue. Potentially, the governing power-law
parameter of these distributions could be used as a biomarker for tissue
disease or pathology.
