Three-dimensional alignment of scans in a dynamic PET study using sinusoidal trajectory signals of a sinogram

A new alignment technique for sequences of three-dimensional (3-D) tomographic data is described. This kind of demand is, for example, in list mode acquisition of positron emission tomography (PET) or gated PET, assuming that distributions during separate scans are nearly equal. A 3-D stackgram is a stack of backprojected projections. Signals parallel to the stackgram´s vertical axis are sinusoidal trajectory signals or locus-signals of the sinogram, which form the points of the object in the image domain. Transformation from the sinogram to the stackgram and back can be implemented in such a way that it is perfectly reversible even in the discrete case. The locus-signals, or locus-vectors in the discrete case, can be processed independently in the stackgram domain. The new local alignment technique is based on similarity comparisons between the locus-vectors in a 3-D neighborhood of sequences of the stackgrams. The final results are aligned sinograms (Method 1), or alternatively, the stackgrams can be summed directly to filtered backprojection images after the alignment (Method 2). The new technique does not require any external movement tracking system or landmarks, and it can be implemented to be fully automatic. In addition, the alignment is done prior to image reconstruction. In this study, the technique is tested using simulated data.