The similarity of a reference patch P_{i;k} with another patch Pj_{;l}(d) associated with the d-th subject is characterized by weight

where Z_{i;k} is a normalization constant to ensure that the weights sum to one. Here й_{м}(г, к) is a parameter that controls the attenuation of the exponential function. As

in [8], we set /г_{м}(г, к) = ^2pdf_{k}M(Vi__{k}), where ft is a constant [8] and df_{k} is the estimated noise standard deviation, which can be computed globally as shown in [9] or spatial-adaptively as shown in [8]. The former is used in this paper. Parameter /г_{х} = flct_{x} controls the attenuation of the second exponential function, where ct_{x} is a scale parameter. |M(P _{i;k})| denotes the length of the vector M(P_{i;k}).

Given D subjects, a “mean” signal can be computed based on the weights resulting from patch matching:

where S(x_{i}, q_{k}; d) is the measured signal associated with the d-th subject at location x_{i} e R^{3} with wavevector q_{k} e R^{3}. V_{i;k} is a local x-q space neighborhood associated with (x_{i}, q_{k}), defined by a radius r_{s} in x-space and an angle a_{s} in q-space. Note the bias associated with the Rician noise distribution is removed in this process [9]. a is the Gaussian noise standard deviation that can be estimated from the image background [9]. Without patch matching, a “simple averaging” version of (6) is given as