Ucl Business Plc

Pankaj Daga

Sebastien Ourselin

An apparatus and method are provided for performing phase unwrapping for an acquired magnetic resonance (MR) image. The method includes modelling the MR phase in the MR image using a Markov random field (MRF) in which the true phase &#x3c6;(t) and the wrapped phase &#x3c6;(w) are modelled as random variables such that at voxel i of said MR image &#x3c6;(t)(i)=&#x3c6;(w)(i)+2&#x3c0;n(i), where n(i) is an unknown integer that needs to be estimated for each voxel i. The method further includes constructing a graph consisting of a set of vertices V and edges E and two special terminal vertices representing a source s and sink t, where there is a one-to-one correspondence between cuts on the graph and configurations of the MRF, a cut representing a partition of the vertices V into disjoint sets S and T such that s&#x3b5;S and t&#x3b5;T. The method further includes finding the minimum energy configuration, E(n(i)|&#x3c6;(w)) of the MRF on the basis that the total cost of a given cut represents the energy of the corresponding MRF configuration, where the cost of a cut is the sum of all edges going from S to T across the cut boundary. The method further includes using the values of n(i) in the minimum energy configuration to perform the phase unwrapping from &#x3c6;(w) to &#x3c6;(t) for the MR image. A confidence may be computed for each voxel using dynamic graph cuts. The unwrapped phase from two MR images acquired at different times may be used to estimate a field map from the phase difference between the two MR images. The field map may be converted into a deformation field which is then used to initialize a non-rigid image registration of the acquired MR image against a reference image. The deformation field of the non-rigid registration is controlled to be smoother where the confidence is high.

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Pankaj Daga