There is great interest to quantify the spectrum of diffusivities that underlie the observed diffusion signal decay; separate tissue compartments can be identified by their spectral peaks. This spectrum is defined by the inverse Laplace transform, but unfortunately this transform is very sensitive to noise omnipresent in diffusion MRI. We present a Bayesian method of inverse Laplace transform that uses Gibbs sampling to provide spectra along with an estimate of the noise related uncertainty in the spectra; this uncertainty information is valuable in interpreting the results. This is applied to multi-b high SNR endorectal coil diffusion data of the prostate.
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