How to obtain high-accuracy image registration: application to movement correction of dynamic positron emission tomography data

When registering dynamic positron emission tomography (PET) sequences, the time-dependent changes in uptake pattern prevent registration of all frames to the first frame in a straightforward manner. Instead, a sequential registration of each frame to its predecessor may be used, provided the registration algorithm is completely free of bias. It is shown that most existing algorithms introduce a bias, the size of which depends on the pixel size and the signal-to-noise ratio or the data. The bias is introduced by the pixelisation of the underlying continuous process. All existing cost-functions are more or less sensitive to noise, and the noise reduction resulting from translating one image set relative to the other means that a small movement will always be detected in the cases where no actual movement has occurred. The problem is solved by an initial resampling of the reference volume into a representation with another image and pixel size. If the new representation is sensibly chosen it means that all possible transforms applied to the other image volume will yield approximately the same noise reduction, thereby removing the source of the bias. The described effect is demonstrated on phantom data, and its impact is shown on human data.