An SVD study of truncated transmission data in SPECT

Even though a noiseless, band-limited function is uniquely determined by its values in a local region, single photon emission computed tomography (SPECT) projections are not band-limited, and unmeasured projections may not be possible to be exactly estimated from the measured data. Projections from all views should be considered simultaneously and are modeled as a set of linear equations. The singular value decomposition (SVD) method is used to analyze and solve the equations. It is shown that truncation does not always result in an underdetermined problem, yet the problem may be ill-conditioned. An inaccurate pixel model may cause reconstruction artifacts via mismatch between the measured data and the modeled projections.