Evaluation of the local shift-invariance approximation in pinhole SPECT

The local shift-invariance approximation of the Fisher information matrix is commonly used in 3D PET and SPECT to speed up the analytical estimation of the contrast recovery coefficient and variance at voxels of interest in a reconstructed image. However, the approximation should only be used under specific conditions, which are usually assumed to be valid. In this work we investigate the two main assumptions behind this approach in a single-pinhole SPECT system, by analyzing Fisher Information Matrix column images. Our results show that the first assumption (localness) is less applicable when low angular sampling is used, and consequently also for highly non-uniform sampling strategies. With the second assumption (local shift-invariance), on the other hand, there seem to be issues in any angular sampling strategy. This indicates that the local shift-invariance approach might not be applicable in many other situations, even for very simple systems and phantoms, particularly in pinhole SPECT. Our findings are mainly intended to show that the local shift-invariance approximation should be used with care. One should always make sure that the assumptions made, as well as any additional approximations, are valid for a particular imaging system, phantom and protocol.