Variable sinograms and redundant information in tomographic imaging

We introduce and illustrate the novel concept of n- and q-variable sinograms, quantities that can be derived from sinogram data in tomographic imaging. The q-variable sinogram unravels the redundant information in sinogram data that arise in numerous tomographic imaging modalities. To demonstrate the utility of the variable sinograms, we focus on SPECT with non-uniform attenuation, deriving both n- and q-sinograms for an off-center Gaussian activity distribution with a linearly varying attenuator. We identify the redundant information in the data function, and show that this redundancy can be exploited to reduce the scanning angle from 2π down to π.