Home Computer Science Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016
The similarity of a reference patch Pi;k with another patch Pj;l(d) associated with the d-th subject is characterized by weight
where Zi;k is a normalization constant to ensure that the weights sum to one. Here йм(г, к) is a parameter that controls the attenuation of the exponential function. As
in , we set /гм(г, к) = ^2pdfkM(Vi_k), where ft is a constant  and dfk is the estimated noise standard deviation, which can be computed globally as shown in  or spatial-adaptively as shown in . The former is used in this paper. Parameter /гх = flctx controls the attenuation of the second exponential function, where ctx is a scale parameter. |M(P i;k)| denotes the length of the vector M(Pi;k).
Given D subjects, a “mean” signal can be computed based on the weights resulting from patch matching:
where S(xi, qk; d) is the measured signal associated with the d-th subject at location xi e R3 with wavevector qk e R3. Vi;k is a local x-q space neighborhood associated with (xi, qk), defined by a radius rs in x-space and an angle as in q-space. Note the bias associated with the Rician noise distribution is removed in this process . a is the Gaussian noise standard deviation that can be estimated from the image background . Without patch matching, a “simple averaging” version of (6) is given as
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