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Phase unwrapping

IP.com Disclosure Number: IPCOM000183913D
Publication Date: 2009-Jun-05
Document File: 5 page(s) / 399K

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In the extraction of a continuous function (called "disturbing function" below) from an N- dimensional array of voxels, each voxel represents a number of discrete possibilities for that disturbing function, or whereby each voxel represents a probability density of the disturbing function, that probability density having a multiplicity of local maxima.
(But since this precise description of the problem contains too much jargon, this is clarified with an example).

In one example of the problem field, we regard out-of-phase Dixon water-fat imaging - an example where the word "phase" is appropriate (a different example will follow a few pages later).

In this problem, we run an MR sequence that is arranged such that it maximally distinguishes "water" and "fat" - "water" referring to all tissue where the majority of the signal is formed by H2O-bound protons, and "fat" referring to tissue where -CH2- bound protons are in the majority. The sequence is arranged such that "fat"-regions get a signal phase that is offset by 180 degrees compared to "water"-regions.

On top of this wanted effect, we always get an additional phase component, which is caused by a disturbing function. This disturbing function is caused mainly by a spatial non-uniformity of the main magnetic field of the magnet, a non-uniformity that is often patient-induced.

In this document, we regard this disturbing function as the unknown function that is to be estimated (although this is not something that is of interest to the end-user, but knowing the error, one can easily calculate the interesting stuff).

Having acquired such an out-of-phase image, every single voxel will give an indication of that disturbing function. However: it gives a whole list (theoretically speaking, an infinite number) of possibilities: if the measured phase of the voxel is 30º, the disturbing function may be 30º (assuming a majority of water-protons), but it may also be -150 º (assuming fat), or 210º (still assuming fat), or 390º, or 570º etc.

These ambiguities are always resolved by assuming the constraint that this disturbing function is continuous in space. (Although, strictly speaking, this assumption is not fully true.)

Many existing algorithms nowadays rely on some kind of region-growing technique: the disturbing function is declared to be known in the "starting pixel"; for "untreated" neighboring pixels thereof, the value of the disturbing function is assigned in order to have a minimal difference to the function at "treated" points.

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Most algorithms suffer from a lack of robustness. An example "water" image is given below. The region-growing obviously failed on one of the shoulders, where water and fat have been swapped. The region-growing is done in a volume that has (at least) one dimension more than the dimensionality of the set of input voxels, one of t...